Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,6,Mod(2,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.2");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.40575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10768x^{12} + 16341006x^{8} + 4217167600x^{4} + 50906640625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{10}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.5 | ||
Root | \(-2.96509 + 2.96509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.8 |
Dual form | 15.6.e.a.2.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.879873 | + | 0.879873i | 0.155541 | + | 0.155541i | 0.780588 | − | 0.625046i | \(-0.214920\pi\) |
−0.625046 | + | 0.780588i | \(0.714920\pi\) | |||||||
\(3\) | 0.0935382 | − | 15.5882i | 0.00600048 | − | 0.999982i | ||||
\(4\) | − | 30.4516i | − | 0.951614i | ||||||
\(5\) | 51.8842 | + | 20.8094i | 0.928133 | + | 0.372250i | ||||
\(6\) | 13.7979 | − | 13.6333i | 0.156472 | − | 0.154605i | ||||
\(7\) | −11.3356 | + | 11.3356i | −0.0874375 | + | 0.0874375i | −0.749473 | − | 0.662035i | \(-0.769693\pi\) |
0.662035 | + | 0.749473i | \(0.269693\pi\) | |||||||
\(8\) | 54.9495 | − | 54.9495i | 0.303556 | − | 0.303556i | ||||
\(9\) | −242.983 | − | 2.91618i | −0.999928 | − | 0.0120007i | ||||
\(10\) | 27.3419 | + | 63.9612i | 0.0864626 | + | 0.202263i | ||||
\(11\) | 359.671i | 0.896238i | 0.893974 | + | 0.448119i | \(0.147906\pi\) | ||||
−0.893974 | + | 0.448119i | \(0.852094\pi\) | |||||||
\(12\) | −474.686 | − | 2.84839i | −0.951597 | − | 0.00571014i | ||||
\(13\) | 370.007 | + | 370.007i | 0.607228 | + | 0.607228i | 0.942221 | − | 0.334993i | \(-0.108734\pi\) |
−0.334993 | + | 0.942221i | \(0.608734\pi\) | |||||||
\(14\) | −19.9477 | −0.0272003 | ||||||||
\(15\) | 329.234 | − | 806.833i | 0.377812 | − | 0.925882i | ||||
\(16\) | −877.755 | −0.857183 | ||||||||
\(17\) | 1244.30 | + | 1244.30i | 1.04425 | + | 1.04425i | 0.998975 | + | 0.0452720i | \(0.0144155\pi\) |
0.0452720 | + | 0.998975i | \(0.485585\pi\) | |||||||
\(18\) | −211.228 | − | 216.360i | −0.153663 | − | 0.157397i | ||||
\(19\) | − | 2005.02i | − | 1.27419i | −0.770784 | − | 0.637096i | \(-0.780135\pi\) | ||
0.770784 | − | 0.637096i | \(-0.219865\pi\) | |||||||
\(20\) | 633.681 | − | 1579.96i | 0.354238 | − | 0.883224i | ||||
\(21\) | 175.640 | + | 177.761i | 0.0869113 | + | 0.0879606i | ||||
\(22\) | −316.465 | + | 316.465i | −0.139402 | + | 0.139402i | ||||
\(23\) | 245.087 | − | 245.087i | 0.0966051 | − | 0.0966051i | −0.657153 | − | 0.753758i | \(-0.728239\pi\) |
0.753758 | + | 0.657153i | \(0.228239\pi\) | |||||||
\(24\) | −851.423 | − | 861.703i | −0.301729 | − | 0.305372i | ||||
\(25\) | 2258.94 | + | 2159.36i | 0.722860 | + | 0.690995i | ||||
\(26\) | 651.119i | 0.188898i | ||||||||
\(27\) | −68.1861 | + | 3787.38i | −0.0180006 | + | 0.999838i | ||||
\(28\) | 345.186 | + | 345.186i | 0.0832067 | + | 0.0832067i | ||||
\(29\) | −7056.79 | −1.55816 | −0.779081 | − | 0.626924i | \(-0.784314\pi\) | ||||
−0.779081 | + | 0.626924i | \(0.784314\pi\) | |||||||
\(30\) | 999.595 | − | 420.227i | 0.202778 | − | 0.0852474i | ||||
\(31\) | −3032.57 | −0.566770 | −0.283385 | − | 0.959006i | \(-0.591457\pi\) | ||||
−0.283385 | + | 0.959006i | \(0.591457\pi\) | |||||||
\(32\) | −2530.70 | − | 2530.70i | −0.436883 | − | 0.436883i | ||||
\(33\) | 5606.61 | + | 33.6430i | 0.896222 | + | 0.00537786i | ||||
\(34\) | 2189.65i | 0.324847i | ||||||||
\(35\) | −824.022 | + | 352.250i | −0.113702 | + | 0.0486050i | ||||
\(36\) | −88.8025 | + | 7399.22i | −0.0114201 | + | 0.951545i | ||||
\(37\) | 2362.96 | − | 2362.96i | 0.283761 | − | 0.283761i | −0.550846 | − | 0.834607i | \(-0.685695\pi\) |
0.834607 | + | 0.550846i | \(0.185695\pi\) | |||||||
\(38\) | 1764.17 | − | 1764.17i | 0.198189 | − | 0.198189i | ||||
\(39\) | 5802.34 | − | 5733.13i | 0.610860 | − | 0.603573i | ||||
\(40\) | 3994.48 | − | 1707.55i | 0.394739 | − | 0.168742i | ||||
\(41\) | − | 6435.18i | − | 0.597862i | −0.954275 | − | 0.298931i | \(-0.903370\pi\) | ||
0.954275 | − | 0.298931i | \(-0.0966301\pi\) | |||||||
\(42\) | −1.86587 | + | 310.948i | −0.000163215 | + | 0.0271998i | ||||
\(43\) | −9718.91 | − | 9718.91i | −0.801579 | − | 0.801579i | 0.181763 | − | 0.983342i | \(-0.441820\pi\) |
−0.983342 | + | 0.181763i | \(0.941820\pi\) | |||||||
\(44\) | 10952.6 | 0.852873 | ||||||||
\(45\) | −12546.3 | − | 5207.62i | −0.923598 | − | 0.383361i | ||||
\(46\) | 431.291 | 0.0300521 | ||||||||
\(47\) | 1492.86 | + | 1492.86i | 0.0985767 | + | 0.0985767i | 0.754675 | − | 0.656099i | \(-0.227794\pi\) |
−0.656099 | + | 0.754675i | \(0.727794\pi\) | |||||||
\(48\) | −82.1037 | + | 13682.6i | −0.00514351 | + | 0.857168i | ||||
\(49\) | 16550.0i | 0.984709i | ||||||||
\(50\) | 87.6175 | + | 3887.54i | 0.00495639 | + | 0.219913i | ||||
\(51\) | 19512.8 | − | 19280.0i | 1.05049 | − | 1.03796i | ||||
\(52\) | 11267.3 | − | 11267.3i | 0.577846 | − | 0.577846i | ||||
\(53\) | −18730.5 | + | 18730.5i | −0.915925 | + | 0.915925i | −0.996730 | − | 0.0808054i | \(-0.974251\pi\) |
0.0808054 | + | 0.996730i | \(0.474251\pi\) | |||||||
\(54\) | −3392.41 | + | 3272.42i | −0.158316 | + | 0.152716i | ||||
\(55\) | −7484.54 | + | 18661.2i | −0.333625 | + | 0.831828i | ||||
\(56\) | 1245.77i | 0.0530844i | ||||||||
\(57\) | −31254.6 | − | 187.546i | −1.27417 | − | 0.00764577i | ||||
\(58\) | −6209.09 | − | 6209.09i | −0.242358 | − | 0.242358i | ||||
\(59\) | 21245.6 | 0.794584 | 0.397292 | − | 0.917692i | \(-0.369950\pi\) | ||||
0.397292 | + | 0.917692i | \(0.369950\pi\) | |||||||
\(60\) | −24569.4 | − | 10025.7i | −0.881082 | − | 0.359532i | ||||
\(61\) | −691.744 | −0.0238024 | −0.0119012 | − | 0.999929i | \(-0.503788\pi\) | ||||
−0.0119012 | + | 0.999929i | \(0.503788\pi\) | |||||||
\(62\) | −2668.28 | − | 2668.28i | −0.0881560 | − | 0.0881560i | ||||
\(63\) | 2787.40 | − | 2721.29i | 0.0884805 | − | 0.0863819i | ||||
\(64\) | 23634.8i | 0.721276i | ||||||||
\(65\) | 11497.9 | + | 26897.1i | 0.337547 | + | 0.789628i | ||||
\(66\) | 4903.51 | + | 4962.71i | 0.138563 | + | 0.140236i | ||||
\(67\) | 40533.4 | − | 40533.4i | 1.10313 | − | 1.10313i | 0.109098 | − | 0.994031i | \(-0.465204\pi\) |
0.994031 | − | 0.109098i | \(-0.0347961\pi\) | |||||||
\(68\) | 37891.0 | − | 37891.0i | 0.993720 | − | 0.993720i | ||||
\(69\) | −3797.53 | − | 3843.38i | −0.0960237 | − | 0.0971831i | ||||
\(70\) | −1034.97 | − | 415.100i | −0.0252454 | − | 0.0101253i | ||||
\(71\) | 8449.81i | 0.198930i | 0.995041 | + | 0.0994652i | \(0.0317132\pi\) | ||||
−0.995041 | + | 0.0994652i | \(0.968287\pi\) | |||||||
\(72\) | −13512.0 | + | 13191.5i | −0.307177 | + | 0.299891i | ||||
\(73\) | −11657.9 | − | 11657.9i | −0.256043 | − | 0.256043i | 0.567399 | − | 0.823443i | \(-0.307950\pi\) |
−0.823443 | + | 0.567399i | \(0.807950\pi\) | |||||||
\(74\) | 4158.21 | 0.0882729 | ||||||||
\(75\) | 33871.7 | − | 35010.7i | 0.695320 | − | 0.718701i | ||||
\(76\) | −61056.2 | −1.21254 | ||||||||
\(77\) | −4077.07 | − | 4077.07i | −0.0783649 | − | 0.0783649i | ||||
\(78\) | 10149.8 | + | 60.9045i | 0.188894 | + | 0.00113348i | ||||
\(79\) | − | 29899.1i | − | 0.539002i | −0.963000 | − | 0.269501i | \(-0.913141\pi\) | ||
0.963000 | − | 0.269501i | \(-0.0868588\pi\) | |||||||
\(80\) | −45541.6 | − | 18265.6i | −0.795579 | − | 0.319086i | ||||
\(81\) | 59032.0 | + | 1417.16i | 0.999712 | + | 0.0239998i | ||||
\(82\) | 5662.15 | − | 5662.15i | 0.0929922 | − | 0.0929922i | ||||
\(83\) | −30668.9 | + | 30668.9i | −0.488656 | + | 0.488656i | −0.907882 | − | 0.419226i | \(-0.862301\pi\) |
0.419226 | + | 0.907882i | \(0.362301\pi\) | |||||||
\(84\) | 5413.11 | − | 5348.54i | 0.0837045 | − | 0.0827060i | ||||
\(85\) | 38666.4 | + | 90452.7i | 0.580479 | + | 1.35792i | ||||
\(86\) | − | 17102.8i | − | 0.249357i | ||||||
\(87\) | −660.080 | + | 110003.i | −0.00934972 | + | 1.55813i | ||||
\(88\) | 19763.8 | + | 19763.8i | 0.272059 | + | 0.272059i | ||||
\(89\) | −106026. | −1.41886 | −0.709428 | − | 0.704778i | \(-0.751047\pi\) | ||||
−0.709428 | + | 0.704778i | \(0.751047\pi\) | |||||||
\(90\) | −6457.08 | − | 15621.2i | −0.0840291 | − | 0.203286i | ||||
\(91\) | −8388.47 | −0.106189 | ||||||||
\(92\) | −7463.29 | − | 7463.29i | −0.0919308 | − | 0.0919308i | ||||
\(93\) | −283.661 | + | 47272.3i | −0.00340089 | + | 0.566760i | ||||
\(94\) | 2627.06i | 0.0306655i | ||||||||
\(95\) | 41723.3 | − | 104029.i | 0.474318 | − | 1.18262i | ||||
\(96\) | −39685.7 | + | 39212.3i | −0.439497 | + | 0.434254i | ||||
\(97\) | −33142.7 | + | 33142.7i | −0.357651 | + | 0.357651i | −0.862946 | − | 0.505296i | \(-0.831383\pi\) |
0.505296 | + | 0.862946i | \(0.331383\pi\) | |||||||
\(98\) | −14561.9 | + | 14561.9i | −0.153163 | + | 0.153163i | ||||
\(99\) | 1048.87 | − | 87393.7i | 0.0107555 | − | 0.896174i | ||||
\(100\) | 65756.0 | − | 68788.4i | 0.657560 | − | 0.687884i | ||||
\(101\) | 13738.7i | 0.134012i | 0.997753 | + | 0.0670060i | \(0.0213447\pi\) | ||||
−0.997753 | + | 0.0670060i | \(0.978655\pi\) | |||||||
\(102\) | 34132.7 | + | 204.816i | 0.324841 | + | 0.00194924i | ||||
\(103\) | −45415.8 | − | 45415.8i | −0.421807 | − | 0.421807i | 0.464019 | − | 0.885825i | \(-0.346407\pi\) |
−0.885825 | + | 0.464019i | \(0.846407\pi\) | |||||||
\(104\) | 40663.4 | 0.368656 | ||||||||
\(105\) | 5413.86 | + | 12878.0i | 0.0479218 | + | 0.113992i | ||||
\(106\) | −32960.9 | −0.284928 | ||||||||
\(107\) | 47232.9 | + | 47232.9i | 0.398828 | + | 0.398828i | 0.877819 | − | 0.478992i | \(-0.158998\pi\) |
−0.478992 | + | 0.877819i | \(0.658998\pi\) | |||||||
\(108\) | 115332. | + | 2076.38i | 0.951460 | + | 0.0171296i | ||||
\(109\) | − | 57758.8i | − | 0.465642i | −0.972520 | − | 0.232821i | \(-0.925204\pi\) | ||
0.972520 | − | 0.232821i | \(-0.0747956\pi\) | |||||||
\(110\) | −23005.0 | + | 9834.08i | −0.181276 | + | 0.0774911i | ||||
\(111\) | −36613.2 | − | 37055.3i | −0.282053 | − | 0.285458i | ||||
\(112\) | 9949.85 | − | 9949.85i | 0.0749499 | − | 0.0749499i | ||||
\(113\) | 136180. | − | 136180.i | 1.00327 | − | 1.00327i | 0.00327423 | − | 0.999995i | \(-0.498958\pi\) |
0.999995 | − | 0.00327423i | \(-0.00104222\pi\) | |||||||
\(114\) | −27335.1 | − | 27665.1i | −0.196997 | − | 0.199375i | ||||
\(115\) | 17816.2 | − | 7616.02i | 0.125624 | − | 0.0537011i | ||||
\(116\) | 214891.i | 1.48277i | ||||||||
\(117\) | −88826.2 | − | 90984.2i | −0.599897 | − | 0.614471i | ||||
\(118\) | 18693.5 | + | 18693.5i | 0.123590 | + | 0.123590i | ||||
\(119\) | −28209.7 | −0.182613 | ||||||||
\(120\) | −26243.9 | − | 62426.4i | −0.166370 | − | 0.395745i | ||||
\(121\) | 31687.8 | 0.196757 | ||||||||
\(122\) | −608.647 | − | 608.647i | −0.00370225 | − | 0.00370225i | ||||
\(123\) | −100313. | − | 601.936i | −0.597852 | − | 0.00358746i | ||||
\(124\) | 92346.8i | 0.539346i | ||||||||
\(125\) | 72268.2 | + | 159044.i | 0.413687 | + | 0.910419i | ||||
\(126\) | 4846.94 | + | 58.1711i | 0.0271983 | + | 0.000326423i | ||||
\(127\) | −70532.8 | + | 70532.8i | −0.388044 | + | 0.388044i | −0.873989 | − | 0.485945i | \(-0.838476\pi\) |
0.485945 | + | 0.873989i | \(0.338476\pi\) | |||||||
\(128\) | −101778. | + | 101778.i | −0.549072 | + | 0.549072i | ||||
\(129\) | −152409. | + | 150591.i | −0.806375 | + | 0.796755i | ||||
\(130\) | −13549.4 | + | 33782.8i | −0.0703172 | + | 0.175322i | ||||
\(131\) | − | 312818.i | − | 1.59263i | −0.604884 | − | 0.796314i | \(-0.706781\pi\) | ||
0.604884 | − | 0.796314i | \(-0.293219\pi\) | |||||||
\(132\) | 1024.48 | − | 170731.i | 0.00511765 | − | 0.852858i | ||||
\(133\) | 22728.0 | + | 22728.0i | 0.111412 | + | 0.111412i | ||||
\(134\) | 71328.6 | 0.343164 | ||||||||
\(135\) | −82350.9 | + | 195086.i | −0.388897 | + | 0.921281i | ||||
\(136\) | 136748. | 0.633975 | ||||||||
\(137\) | 44151.7 | + | 44151.7i | 0.200977 | + | 0.200977i | 0.800418 | − | 0.599442i | \(-0.204611\pi\) |
−0.599442 | + | 0.800418i | \(0.704611\pi\) | |||||||
\(138\) | 40.3422 | − | 6723.03i | 0.000180327 | − | 0.0300516i | ||||
\(139\) | 10378.2i | 0.0455600i | 0.999741 | + | 0.0227800i | \(0.00725173\pi\) | ||||
−0.999741 | + | 0.0227800i | \(0.992748\pi\) | |||||||
\(140\) | 10726.6 | + | 25092.8i | 0.0462532 | + | 0.108201i | ||||
\(141\) | 23410.6 | − | 23131.3i | 0.0991665 | − | 0.0979834i | ||||
\(142\) | −7434.76 | + | 7434.76i | −0.0309419 | + | 0.0309419i | ||||
\(143\) | −133081. | + | 133081.i | −0.544221 | + | 0.544221i | ||||
\(144\) | 213279. | + | 2559.69i | 0.857121 | + | 0.0102868i | ||||
\(145\) | −366136. | − | 146848.i | −1.44618 | − | 0.580025i | ||||
\(146\) | − | 20515.0i | − | 0.0796505i | ||||||
\(147\) | 257984. | + | 1548.06i | 0.984692 | + | 0.00590873i | ||||
\(148\) | −71956.1 | − | 71956.1i | −0.270031 | − | 0.270031i | ||||
\(149\) | 357728. | 1.32004 | 0.660019 | − | 0.751249i | \(-0.270548\pi\) | ||||
0.660019 | + | 0.751249i | \(0.270548\pi\) | |||||||
\(150\) | 60607.9 | − | 1002.16i | 0.219938 | − | 0.00363672i | ||||
\(151\) | 181033. | 0.646124 | 0.323062 | − | 0.946378i | \(-0.395288\pi\) | ||||
0.323062 | + | 0.946378i | \(0.395288\pi\) | |||||||
\(152\) | −110175. | − | 110175.i | −0.386789 | − | 0.386789i | ||||
\(153\) | −298715. | − | 305972.i | −1.03164 | − | 1.05670i | ||||
\(154\) | − | 7174.61i | − | 0.0243779i | ||||||
\(155\) | −157342. | − | 63106.0i | −0.526038 | − | 0.210980i | ||||
\(156\) | −174583. | − | 176691.i | −0.574369 | − | 0.581303i | ||||
\(157\) | 190153. | − | 190153.i | 0.615679 | − | 0.615679i | −0.328741 | − | 0.944420i | \(-0.606624\pi\) |
0.944420 | + | 0.328741i | \(0.106624\pi\) | |||||||
\(158\) | 26307.4 | − | 26307.4i | 0.0838370 | − | 0.0838370i | ||||
\(159\) | 290222. | + | 293726.i | 0.910412 | + | 0.921404i | ||||
\(160\) | −78640.9 | − | 183966.i | −0.242856 | − | 0.568116i | ||||
\(161\) | 5556.39i | 0.0168938i | ||||||||
\(162\) | 50693.8 | + | 53187.6i | 0.151763 | + | 0.159229i | ||||
\(163\) | 379306. | + | 379306.i | 1.11820 | + | 1.11820i | 0.992005 | + | 0.126198i | \(0.0402773\pi\) |
0.126198 | + | 0.992005i | \(0.459723\pi\) | |||||||
\(164\) | −195962. | −0.568934 | ||||||||
\(165\) | 290194. | + | 118416.i | 0.829811 | + | 0.338610i | ||||
\(166\) | −53969.5 | −0.152012 | ||||||||
\(167\) | −212126. | − | 212126.i | −0.588576 | − | 0.588576i | 0.348670 | − | 0.937246i | \(-0.386633\pi\) |
−0.937246 | + | 0.348670i | \(0.886633\pi\) | |||||||
\(168\) | 19419.2 | + | 116.527i | 0.0530834 | + | 0.000318532i | ||||
\(169\) | − | 97482.6i | − | 0.262549i | ||||||
\(170\) | −45565.4 | + | 113608.i | −0.120924 | + | 0.301501i | ||||
\(171\) | −5847.01 | + | 487185.i | −0.0152913 | + | 1.27410i | ||||
\(172\) | −295957. | + | 295957.i | −0.762794 | + | 0.762794i | ||||
\(173\) | 52714.4 | − | 52714.4i | 0.133910 | − | 0.133910i | −0.636974 | − | 0.770885i | \(-0.719814\pi\) |
0.770885 | + | 0.636974i | \(0.219814\pi\) | |||||||
\(174\) | −97369.1 | + | 96207.5i | −0.243808 | + | 0.240900i | ||||
\(175\) | −50083.8 | + | 1128.79i | −0.123624 | + | 0.00278624i | ||||
\(176\) | − | 315703.i | − | 0.768240i | ||||||
\(177\) | 1987.28 | − | 331181.i | 0.00476788 | − | 0.794569i | ||||
\(178\) | −93289.7 | − | 93289.7i | −0.220690 | − | 0.220690i | ||||
\(179\) | −524394. | −1.22328 | −0.611639 | − | 0.791137i | \(-0.709490\pi\) | ||||
−0.611639 | + | 0.791137i | \(0.709490\pi\) | |||||||
\(180\) | −158581. | + | 382054.i | −0.364812 | + | 0.878909i | ||||
\(181\) | 163991. | 0.372068 | 0.186034 | − | 0.982543i | \(-0.440437\pi\) | ||||
0.186034 | + | 0.982543i | \(0.440437\pi\) | |||||||
\(182\) | −7380.79 | − | 7380.79i | −0.0165167 | − | 0.0165167i | ||||
\(183\) | −64.7045 | + | 10783.0i | −0.000142826 | + | 0.0238020i | ||||
\(184\) | − | 26934.8i | − | 0.0586502i | ||||||
\(185\) | 171772. | − | 73428.5i | 0.368998 | − | 0.157738i | ||||
\(186\) | −41843.2 | + | 41344.0i | −0.0886834 | + | 0.0876255i | ||||
\(187\) | −447539. | + | 447539.i | −0.935894 | + | 0.935894i | ||||
\(188\) | 45460.0 | − | 45460.0i | 0.0938070 | − | 0.0938070i | ||||
\(189\) | −42159.1 | − | 43705.0i | −0.0858494 | − | 0.0889973i | ||||
\(190\) | 128244. | − | 54821.1i | 0.257722 | − | 0.110170i | ||||
\(191\) | 559164.i | 1.10906i | 0.832163 | + | 0.554531i | \(0.187102\pi\) | ||||
−0.832163 | + | 0.554531i | \(0.812898\pi\) | |||||||
\(192\) | 368423. | + | 2210.76i | 0.721263 | + | 0.00432800i | ||||
\(193\) | 150013. | + | 150013.i | 0.289891 | + | 0.289891i | 0.837037 | − | 0.547146i | \(-0.184286\pi\) |
−0.547146 | + | 0.837037i | \(0.684286\pi\) | |||||||
\(194\) | −58322.8 | −0.111259 | ||||||||
\(195\) | 420353. | − | 176715.i | 0.791640 | − | 0.332803i | ||||
\(196\) | 503975. | 0.937063 | ||||||||
\(197\) | 237011. | + | 237011.i | 0.435113 | + | 0.435113i | 0.890363 | − | 0.455250i | \(-0.150450\pi\) |
−0.455250 | + | 0.890363i | \(0.650450\pi\) | |||||||
\(198\) | 77818.3 | − | 75972.6i | 0.141065 | − | 0.137719i | ||||
\(199\) | − | 602333.i | − | 1.07821i | −0.842238 | − | 0.539106i | \(-0.818762\pi\) | ||
0.842238 | − | 0.539106i | \(-0.181238\pi\) | |||||||
\(200\) | 242783. | − | 5471.86i | 0.429184 | − | 0.00967297i | ||||
\(201\) | −628051. | − | 635633.i | −1.09649 | − | 1.10973i | ||||
\(202\) | −12088.4 | + | 12088.4i | −0.0208444 | + | 0.0208444i | ||||
\(203\) | 79992.7 | − | 79992.7i | 0.136242 | − | 0.136242i | ||||
\(204\) | −587107. | − | 594196.i | −0.987739 | − | 0.999665i | ||||
\(205\) | 133912. | − | 333884.i | 0.222554 | − | 0.554896i | ||||
\(206\) | − | 79920.3i | − | 0.131217i | ||||||
\(207\) | −60266.5 | + | 58837.1i | −0.0977575 | + | 0.0954388i | ||||
\(208\) | −324776. | − | 324776.i | −0.520505 | − | 0.520505i | ||||
\(209\) | 721148. | 1.14198 | ||||||||
\(210\) | −6567.46 | + | 16094.5i | −0.0102766 | + | 0.0251842i | ||||
\(211\) | −905177. | −1.39968 | −0.699838 | − | 0.714302i | \(-0.746744\pi\) | ||||
−0.699838 | + | 0.714302i | \(0.746744\pi\) | |||||||
\(212\) | 570375. | + | 570375.i | 0.871607 | + | 0.871607i | ||||
\(213\) | 131717. | + | 790.380i | 0.198927 | + | 0.00119368i | ||||
\(214\) | 83118.0i | 0.124068i | ||||||||
\(215\) | −302013. | − | 706502.i | −0.445584 | − | 1.04236i | ||||
\(216\) | 204368. | + | 211862.i | 0.298043 | + | 0.308971i | ||||
\(217\) | 34375.9 | − | 34375.9i | 0.0495569 | − | 0.0495569i | ||||
\(218\) | 50820.5 | − | 50820.5i | 0.0724265 | − | 0.0724265i | ||||
\(219\) | −182816. | + | 180635.i | −0.257575 | + | 0.254502i | ||||
\(220\) | 568265. | + | 227916.i | 0.791579 | + | 0.317482i | ||||
\(221\) | 920800.i | 1.26819i | ||||||||
\(222\) | 388.952 | − | 64819.0i | 0.000529680 | − | 0.0882713i | ||||
\(223\) | 325294. | + | 325294.i | 0.438040 | + | 0.438040i | 0.891352 | − | 0.453312i | \(-0.149758\pi\) |
−0.453312 | + | 0.891352i | \(0.649758\pi\) | |||||||
\(224\) | 57373.8 | 0.0764000 | ||||||||
\(225\) | −542585. | − | 531274.i | −0.714516 | − | 0.699620i | ||||
\(226\) | 239642. | 0.312099 | ||||||||
\(227\) | −71799.3 | − | 71799.3i | −0.0924816 | − | 0.0924816i | 0.659352 | − | 0.751834i | \(-0.270831\pi\) |
−0.751834 | + | 0.659352i | \(0.770831\pi\) | |||||||
\(228\) | −5711.09 | + | 951755.i | −0.00727582 | + | 1.21252i | ||||
\(229\) | 278676.i | 0.351165i | 0.984465 | + | 0.175583i | \(0.0561809\pi\) | ||||
−0.984465 | + | 0.175583i | \(0.943819\pi\) | |||||||
\(230\) | 22377.2 | + | 8974.90i | 0.0278924 | + | 0.0111869i | ||||
\(231\) | −63935.4 | + | 63172.7i | −0.0788337 | + | 0.0778932i | ||||
\(232\) | −387768. | + | 387768.i | −0.472990 | + | 0.472990i | ||||
\(233\) | 71640.1 | − | 71640.1i | 0.0864503 | − | 0.0864503i | −0.662559 | − | 0.749010i | \(-0.730530\pi\) |
0.749010 | + | 0.662559i | \(0.230530\pi\) | |||||||
\(234\) | 1898.78 | − | 158210.i | 0.00226691 | − | 0.188884i | ||||
\(235\) | 46390.3 | + | 108521.i | 0.0547971 | + | 0.128187i | ||||
\(236\) | − | 646965.i | − | 0.756137i | ||||||
\(237\) | −466073. | − | 2796.71i | −0.538993 | − | 0.00323427i | ||||
\(238\) | −24821.0 | − | 24821.0i | −0.0284038 | − | 0.0284038i | ||||
\(239\) | −1.08062e6 | −1.22371 | −0.611854 | − | 0.790971i | \(-0.709576\pi\) | ||||
−0.611854 | + | 0.790971i | \(0.709576\pi\) | |||||||
\(240\) | −288987. | + | 708202.i | −0.323854 | + | 0.793650i | ||||
\(241\) | −342370. | −0.379710 | −0.189855 | − | 0.981812i | \(-0.560802\pi\) | ||||
−0.189855 | + | 0.981812i | \(0.560802\pi\) | |||||||
\(242\) | 27881.3 | + | 27881.3i | 0.0306037 | + | 0.0306037i | ||||
\(243\) | 27612.7 | − | 920069.i | 0.0299981 | − | 0.999550i | ||||
\(244\) | 21064.7i | 0.0226507i | ||||||||
\(245\) | −344396. | + | 858684.i | −0.366558 | + | 0.913941i | ||||
\(246\) | −87732.9 | − | 88792.2i | −0.0924325 | − | 0.0935485i | ||||
\(247\) | 741872. | − | 741872.i | 0.773725 | − | 0.773725i | ||||
\(248\) | −166638. | + | 166638.i | −0.172047 | + | 0.172047i | ||||
\(249\) | 475203. | + | 480941.i | 0.485715 | + | 0.491579i | ||||
\(250\) | −76351.4 | + | 203525.i | −0.0772622 | + | 0.205953i | ||||
\(251\) | − | 195789.i | − | 0.196157i | −0.995179 | − | 0.0980787i | \(-0.968730\pi\) | ||
0.995179 | − | 0.0980787i | \(-0.0312697\pi\) | |||||||
\(252\) | −82867.6 | − | 84880.9i | −0.0822022 | − | 0.0841993i | ||||
\(253\) | 88150.6 | + | 88150.6i | 0.0865812 | + | 0.0865812i | ||||
\(254\) | −124120. | −0.120714 | ||||||||
\(255\) | 1.41361e6 | − | 594278.i | 1.36138 | − | 0.572320i | ||||
\(256\) | 577209. | 0.550470 | ||||||||
\(257\) | −614221. | − | 614221.i | −0.580085 | − | 0.580085i | 0.354841 | − | 0.934927i | \(-0.384535\pi\) |
−0.934927 | + | 0.354841i | \(0.884535\pi\) | |||||||
\(258\) | −266602. | − | 1599.77i | −0.249353 | − | 0.00149626i | ||||
\(259\) | 53571.0i | 0.0496227i | ||||||||
\(260\) | 819062. | − | 350130.i | 0.751421 | − | 0.321215i | ||||
\(261\) | 1.71468e6 | + | 20578.9i | 1.55805 | + | 0.0186991i | ||||
\(262\) | 275241. | − | 275241.i | 0.247719 | − | 0.247719i | ||||
\(263\) | 398691. | − | 398691.i | 0.355425 | − | 0.355425i | −0.506699 | − | 0.862123i | \(-0.669134\pi\) |
0.862123 | + | 0.506699i | \(0.169134\pi\) | |||||||
\(264\) | 309930. | − | 306232.i | 0.273686 | − | 0.270421i | ||||
\(265\) | −1.36159e6 | + | 582046.i | −1.19105 | + | 0.509147i | ||||
\(266\) | 39995.6i | 0.0346584i | ||||||||
\(267\) | −9917.51 | + | 1.65276e6i | −0.00851382 | + | 1.41883i | ||||
\(268\) | −1.23431e6 | − | 1.23431e6i | −1.04975 | − | 1.04975i | ||||
\(269\) | 1.29261e6 | 1.08915 | 0.544575 | − | 0.838712i | \(-0.316691\pi\) | ||||
0.544575 | + | 0.838712i | \(0.316691\pi\) | |||||||
\(270\) | −244110. | + | 99192.9i | −0.203787 | + | 0.0828077i | ||||
\(271\) | −785610. | −0.649806 | −0.324903 | − | 0.945747i | \(-0.605332\pi\) | ||||
−0.324903 | + | 0.945747i | \(0.605332\pi\) | |||||||
\(272\) | −1.09219e6 | − | 1.09219e6i | −0.895110 | − | 0.895110i | ||||
\(273\) | −784.643 | + | 130761.i | −0.000637185 | + | 0.106187i | ||||
\(274\) | 77695.7i | 0.0625203i | ||||||||
\(275\) | −776658. | + | 812474.i | −0.619296 | + | 0.647855i | ||||
\(276\) | −117037. | + | 115641.i | −0.0924808 | + | 0.0913775i | ||||
\(277\) | 1.55247e6 | − | 1.55247e6i | 1.21569 | − | 1.21569i | 0.246564 | − | 0.969127i | \(-0.420699\pi\) |
0.969127 | − | 0.246564i | \(-0.0793014\pi\) | |||||||
\(278\) | −9131.49 | + | 9131.49i | −0.00708646 | + | 0.00708646i | ||||
\(279\) | 736862. | + | 8843.53i | 0.566729 | + | 0.00680166i | ||||
\(280\) | −25923.7 | + | 64635.6i | −0.0197607 | + | 0.0492694i | ||||
\(281\) | − | 1.24917e6i | − | 0.943748i | −0.881666 | − | 0.471874i | \(-0.843578\pi\) | ||
0.881666 | − | 0.471874i | \(-0.156422\pi\) | |||||||
\(282\) | 40951.0 | + | 245.730i | 0.0306649 | + | 0.000184008i | ||||
\(283\) | 564054. | + | 564054.i | 0.418654 | + | 0.418654i | 0.884739 | − | 0.466086i | \(-0.154336\pi\) |
−0.466086 | + | 0.884739i | \(0.654336\pi\) | |||||||
\(284\) | 257311. | 0.189305 | ||||||||
\(285\) | −1.61772e6 | − | 660121.i | −1.17975 | − | 0.481406i | ||||
\(286\) | −234188. | −0.169297 | ||||||||
\(287\) | 72946.4 | + | 72946.4i | 0.0522756 | + | 0.0522756i | ||||
\(288\) | 607536. | + | 622296.i | 0.431609 | + | 0.442095i | ||||
\(289\) | 1.67671e6i | 1.18090i | ||||||||
\(290\) | −192946. | − | 451361.i | −0.134723 | − | 0.315158i | ||||
\(291\) | 513535. | + | 519735.i | 0.355498 | + | 0.359790i | ||||
\(292\) | −355002. | + | 355002.i | −0.243654 | + | 0.243654i | ||||
\(293\) | −1.97297e6 | + | 1.97297e6i | −1.34261 | + | 1.34261i | −0.449165 | + | 0.893449i | \(0.648279\pi\) |
−0.893449 | + | 0.449165i | \(0.851721\pi\) | |||||||
\(294\) | 225632. | + | 228356.i | 0.152241 | + | 0.154079i | ||||
\(295\) | 1.10231e6 | + | 442109.i | 0.737479 | + | 0.295784i | ||||
\(296\) | − | 259687.i | − | 0.172275i | ||||||
\(297\) | −1.36221e6 | − | 24524.6i | −0.896093 | − | 0.0161328i | ||||
\(298\) | 314755. | + | 314755.i | 0.205320 | + | 0.205320i | ||||
\(299\) | 181368. | 0.117323 | ||||||||
\(300\) | −1.06613e6 | − | 1.03145e6i | −0.683926 | − | 0.661676i | ||||
\(301\) | 220339. | 0.140176 | ||||||||
\(302\) | 159286. | + | 159286.i | 0.100499 | + | 0.100499i | ||||
\(303\) | 214162. | + | 1285.10i | 0.134010 | + | 0.000804136i | ||||
\(304\) | 1.75992e6i | 1.09222i | ||||||||
\(305\) | −35890.6 | − | 14394.8i | −0.0220918 | − | 0.00886045i | ||||
\(306\) | 6385.43 | − | 532048.i | 0.00389840 | − | 0.324823i | ||||
\(307\) | 712049. | − | 712049.i | 0.431185 | − | 0.431185i | −0.457846 | − | 0.889032i | \(-0.651379\pi\) |
0.889032 | + | 0.457846i | \(0.151379\pi\) | |||||||
\(308\) | −124153. | + | 124153.i | −0.0745731 | + | 0.0745731i | ||||
\(309\) | −712197. | + | 703701.i | −0.424330 | + | 0.419268i | ||||
\(310\) | −82916.2 | − | 193967.i | −0.0490044 | − | 0.114637i | ||||
\(311\) | 801658.i | 0.469990i | 0.971997 | + | 0.234995i | \(0.0755073\pi\) | ||||
−0.971997 | + | 0.234995i | \(0.924493\pi\) | |||||||
\(312\) | 3803.59 | − | 633869.i | 0.00221211 | − | 0.368649i | ||||
\(313\) | −1.36383e6 | − | 1.36383e6i | −0.786862 | − | 0.786862i | 0.194116 | − | 0.980978i | \(-0.437816\pi\) |
−0.980978 | + | 0.194116i | \(0.937816\pi\) | |||||||
\(314\) | 334621. | 0.191527 | ||||||||
\(315\) | 201250. | − | 83187.6i | 0.114277 | − | 0.0472370i | ||||
\(316\) | −910477. | −0.512922 | ||||||||
\(317\) | 1.44550e6 | + | 1.44550e6i | 0.807925 | + | 0.807925i | 0.984320 | − | 0.176394i | \(-0.0564433\pi\) |
−0.176394 | + | 0.984320i | \(0.556443\pi\) | |||||||
\(318\) | −3083.11 | + | 513801.i | −0.00170970 | + | 0.284923i | ||||
\(319\) | − | 2.53812e6i | − | 1.39648i | ||||||
\(320\) | −491826. | + | 1.22627e6i | −0.268495 | + | 0.669440i | ||||
\(321\) | 740693. | − | 731857.i | 0.401214 | − | 0.396428i | ||||
\(322\) | −4888.92 | + | 4888.92i | −0.00262768 | + | 0.00262768i | ||||
\(323\) | 2.49485e6 | − | 2.49485e6i | 1.33057 | − | 1.33057i | ||||
\(324\) | 43154.9 | − | 1.79762e6i | 0.0228385 | − | 0.951340i | ||||
\(325\) | 36845.2 | + | 1.63480e6i | 0.0193496 | + | 0.858532i | ||||
\(326\) | 667482.i | 0.347853i | ||||||||
\(327\) | −900355. | − | 5402.66i | −0.465634 | − | 0.00279408i | ||||
\(328\) | −353610. | − | 353610.i | −0.181485 | − | 0.181485i | ||||
\(329\) | −33844.8 | −0.0172386 | ||||||||
\(330\) | 151143. | + | 359525.i | 0.0764020 | + | 0.181738i | ||||
\(331\) | −167596. | −0.0840801 | −0.0420400 | − | 0.999116i | \(-0.513386\pi\) | ||||
−0.0420400 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(332\) | 933918. | + | 933918.i | 0.465011 | + | 0.465011i | ||||
\(333\) | −581049. | + | 567267.i | −0.287146 | + | 0.280335i | ||||
\(334\) | − | 373288.i | − | 0.183095i | ||||||
\(335\) | 2.94652e6 | − | 1.25957e6i | 1.43449 | − | 0.613210i | ||||
\(336\) | −154169. | − | 156031.i | −0.0744989 | − | 0.0753983i | ||||
\(337\) | −578695. | + | 578695.i | −0.277571 | + | 0.277571i | −0.832139 | − | 0.554567i | \(-0.812884\pi\) |
0.554567 | + | 0.832139i | \(0.312884\pi\) | |||||||
\(338\) | 85772.3 | − | 85772.3i | 0.0408372 | − | 0.0408372i | ||||
\(339\) | −2.11006e6 | − | 2.13554e6i | −0.997231 | − | 1.00927i | ||||
\(340\) | 2.75443e6 | − | 1.17745e6i | 1.29222 | − | 0.552392i | ||||
\(341\) | − | 1.09073e6i | − | 0.507961i | ||||||
\(342\) | −433806. | + | 423517.i | −0.200553 | + | 0.195797i | ||||
\(343\) | −378120. | − | 378120.i | −0.173538 | − | 0.173538i | ||||
\(344\) | −1.06810e6 | −0.486649 | ||||||||
\(345\) | −117053. | − | 278435.i | −0.0529463 | − | 0.125944i | ||||
\(346\) | 92764.1 | 0.0416572 | ||||||||
\(347\) | −55424.5 | − | 55424.5i | −0.0247103 | − | 0.0247103i | 0.694644 | − | 0.719354i | \(-0.255562\pi\) |
−0.719354 | + | 0.694644i | \(0.755562\pi\) | |||||||
\(348\) | 3.34976e6 | + | 20100.5i | 1.48274 | + | 0.00889732i | ||||
\(349\) | 1.16783e6i | 0.513234i | 0.966513 | + | 0.256617i | \(0.0826079\pi\) | ||||
−0.966513 | + | 0.256617i | \(0.917392\pi\) | |||||||
\(350\) | −45060.6 | − | 43074.2i | −0.0196620 | − | 0.0187952i | ||||
\(351\) | −1.42659e6 | + | 1.37613e6i | −0.618060 | + | 0.596199i | ||||
\(352\) | 910219. | − | 910219.i | 0.391552 | − | 0.391552i | ||||
\(353\) | −227606. | + | 227606.i | −0.0972182 | + | 0.0972182i | −0.754043 | − | 0.656825i | \(-0.771899\pi\) |
0.656825 | + | 0.754043i | \(0.271899\pi\) | |||||||
\(354\) | 293146. | − | 289649.i | 0.124330 | − | 0.122847i | ||||
\(355\) | −175836. | + | 438412.i | −0.0740518 | + | 0.184634i | ||||
\(356\) | 3.22867e6i | 1.35020i | ||||||||
\(357\) | −2638.68 | + | 439738.i | −0.00109576 | + | 0.182609i | ||||
\(358\) | −461401. | − | 461401.i | −0.190270 | − | 0.190270i | ||||
\(359\) | −3.03165e6 | −1.24149 | −0.620744 | − | 0.784014i | \(-0.713169\pi\) | ||||
−0.620744 | + | 0.784014i | \(0.713169\pi\) | |||||||
\(360\) | −975568. | + | 403255.i | −0.396736 | + | 0.163992i | ||||
\(361\) | −1.54401e6 | −0.623567 | ||||||||
\(362\) | 144291. | + | 144291.i | 0.0578719 | + | 0.0578719i | ||||
\(363\) | 2964.02 | − | 493956.i | 0.00118063 | − | 0.196753i | ||||
\(364\) | 255443.i | 0.101051i | ||||||||
\(365\) | −362267. | − | 847455.i | −0.142330 | − | 0.332954i | ||||
\(366\) | −9544.63 | + | 9430.77i | −0.00372440 | + | 0.00367997i | ||||
\(367\) | −3.13626e6 | + | 3.13626e6i | −1.21548 | + | 1.21548i | −0.246277 | + | 0.969200i | \(0.579207\pi\) |
−0.969200 | + | 0.246277i | \(0.920793\pi\) | |||||||
\(368\) | −215126. | + | 215126.i | −0.0828083 | + | 0.0828083i | ||||
\(369\) | −18766.2 | + | 1.56364e6i | −0.00717479 | + | 0.597819i | ||||
\(370\) | 215746. | + | 86530.0i | 0.0819290 | + | 0.0328596i | ||||
\(371\) | − | 424641.i | − | 0.160172i | ||||||
\(372\) | 1.43952e6 | + | 8637.96i | 0.539336 | + | 0.00323634i | ||||
\(373\) | 3.09998e6 | + | 3.09998e6i | 1.15368 | + | 1.15368i | 0.985808 | + | 0.167876i | \(0.0536907\pi\) |
0.167876 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(374\) | −787555. | −0.291140 | ||||||||
\(375\) | 2.48596e6 | − | 1.11165e6i | 0.912885 | − | 0.408217i | ||||
\(376\) | 164064. | 0.0598472 | ||||||||
\(377\) | −2.61106e6 | − | 2.61106e6i | −0.946159 | − | 0.946159i | ||||
\(378\) | 1360.16 | − | 75549.6i | 0.000489620 | − | 0.0271958i | ||||
\(379\) | − | 3.76652e6i | − | 1.34692i | −0.739224 | − | 0.673460i | \(-0.764807\pi\) | ||
0.739224 | − | 0.673460i | \(-0.235193\pi\) | |||||||
\(380\) | −3.16785e6 | − | 1.27054e6i | −1.12540 | − | 0.451368i | ||||
\(381\) | 1.09288e6 | + | 1.10607e6i | 0.385709 | + | 0.390366i | ||||
\(382\) | −491993. | + | 491993.i | −0.172505 | + | 0.172505i | ||||
\(383\) | −1.03003e6 | + | 1.03003e6i | −0.358802 | + | 0.358802i | −0.863371 | − | 0.504569i | \(-0.831651\pi\) |
0.504569 | + | 0.863371i | \(0.331651\pi\) | |||||||
\(384\) | 1.57701e6 | + | 1.59605e6i | 0.545767 | + | 0.552356i | ||||
\(385\) | −126694. | − | 296377.i | −0.0435617 | − | 0.101904i | ||||
\(386\) | 263984.i | 0.0901800i | ||||||||
\(387\) | 2.33318e6 | + | 2.38987e6i | 0.791902 | + | 0.811141i | ||||
\(388\) | 1.00925e6 | + | 1.00925e6i | 0.340345 | + | 0.340345i | ||||
\(389\) | 2.93288e6 | 0.982698 | 0.491349 | − | 0.870963i | \(-0.336504\pi\) | ||||
0.491349 | + | 0.870963i | \(0.336504\pi\) | |||||||
\(390\) | 525344. | + | 214370.i | 0.174897 | + | 0.0713679i | ||||
\(391\) | 609923. | 0.201759 | ||||||||
\(392\) | 909416. | + | 909416.i | 0.298915 | + | 0.298915i | ||||
\(393\) | −4.87627e6 | − | 29260.5i | −1.59260 | − | 0.00955653i | ||||
\(394\) | 417079.i | 0.135356i | ||||||||
\(395\) | 622183. | − | 1.55129e6i | 0.200644 | − | 0.500266i | ||||
\(396\) | −2.66128e6 | − | 31939.7i | −0.852812 | − | 0.0102351i | ||||
\(397\) | 2.33959e6 | − | 2.33959e6i | 0.745013 | − | 0.745013i | −0.228525 | − | 0.973538i | \(-0.573390\pi\) |
0.973538 | + | 0.228525i | \(0.0733902\pi\) | |||||||
\(398\) | 529977. | − | 529977.i | 0.167706 | − | 0.167706i | ||||
\(399\) | 356415. | − | 352163.i | 0.112079 | − | 0.110742i | ||||
\(400\) | −1.98279e6 | − | 1.89539e6i | −0.619623 | − | 0.592309i | ||||
\(401\) | − | 3.56068e6i | − | 1.10579i | −0.833251 | − | 0.552895i | \(-0.813523\pi\) | ||
0.833251 | − | 0.552895i | \(-0.186477\pi\) | |||||||
\(402\) | 6671.95 | − | 1.11188e6i | 0.00205915 | − | 0.343158i | ||||
\(403\) | −1.12207e6 | − | 1.12207e6i | −0.344158 | − | 0.344158i | ||||
\(404\) | 418367. | 0.127528 | ||||||||
\(405\) | 3.03334e6 | + | 1.30195e6i | 0.918931 | + | 0.394418i | ||||
\(406\) | 140767. | 0.0423824 | ||||||||
\(407\) | 849888. | + | 849888.i | 0.254317 | + | 0.254317i | ||||
\(408\) | 12791.1 | − | 2.13164e6i | 0.00380416 | − | 0.633964i | ||||
\(409\) | − | 2.99031e6i | − | 0.883910i | −0.897037 | − | 0.441955i | \(-0.854285\pi\) | ||
0.897037 | − | 0.441955i | \(-0.145715\pi\) | |||||||
\(410\) | 411602. | − | 175950.i | 0.120925 | − | 0.0516927i | ||||
\(411\) | 692374. | − | 684114.i | 0.202179 | − | 0.199767i | ||||
\(412\) | −1.38298e6 | + | 1.38298e6i | −0.401397 | + | 0.401397i | ||||
\(413\) | −240831. | + | 240831.i | −0.0694764 | + | 0.0694764i | ||||
\(414\) | −104796. | − | 1257.72i | −0.0300500 | − | 0.000360648i | ||||
\(415\) | −2.22943e6 | + | 953029.i | −0.635439 | + | 0.271635i | ||||
\(416\) | − | 1.87275e6i | − | 0.530575i | ||||||
\(417\) | 161777. | + | 970.757i | 0.0455592 | + | 0.000273382i | ||||
\(418\) | 634519. | + | 634519.i | 0.177625 | + | 0.177625i | ||||
\(419\) | −552976. | −0.153876 | −0.0769381 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769381 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(420\) | 392155. | − | 164861.i | 0.108476 | − | 0.0456031i | ||||
\(421\) | 5.56113e6 | 1.52918 | 0.764588 | − | 0.644519i | \(-0.222942\pi\) | ||||
0.764588 | + | 0.644519i | \(0.222942\pi\) | |||||||
\(422\) | −796441. | − | 796441.i | −0.217707 | − | 0.217707i | ||||
\(423\) | −358385. | − | 367092.i | −0.0973866 | − | 0.0997526i | ||||
\(424\) | 2.05846e6i | 0.556069i | ||||||||
\(425\) | 123907. | + | 5.49769e6i | 0.0332754 | + | 1.47641i | ||||
\(426\) | 115199. | + | 116590.i | 0.0307556 | + | 0.0311270i | ||||
\(427\) | 7841.31 | − | 7841.31i | 0.00208122 | − | 0.00208122i | ||||
\(428\) | 1.43832e6 | − | 1.43832e6i | 0.379530 | − | 0.379530i | ||||
\(429\) | 2.06204e6 | + | 2.08693e6i | 0.540945 | + | 0.547477i | ||||
\(430\) | 355900. | − | 887366.i | 0.0928231 | − | 0.231436i | ||||
\(431\) | 3.18200e6i | 0.825100i | 0.910935 | + | 0.412550i | \(0.135362\pi\) | ||||
−0.910935 | + | 0.412550i | \(0.864638\pi\) | |||||||
\(432\) | 59850.7 | − | 3.32439e6i | 0.0154298 | − | 0.857044i | ||||
\(433\) | −506874. | − | 506874.i | −0.129921 | − | 0.129921i | 0.639156 | − | 0.769077i | \(-0.279284\pi\) |
−0.769077 | + | 0.639156i | \(0.779284\pi\) | |||||||
\(434\) | 60492.9 | 0.0154163 | ||||||||
\(435\) | −2.32334e6 | + | 5.69366e6i | −0.588693 | + | 1.44267i | ||||
\(436\) | −1.75885e6 | −0.443111 | ||||||||
\(437\) | −491404. | − | 491404.i | −0.123094 | − | 0.123094i | ||||
\(438\) | −319791. | − | 1918.93i | −0.0796491 | − | 0.000477941i | ||||
\(439\) | 4.28320e6i | 1.06074i | 0.847767 | + | 0.530368i | \(0.177946\pi\) | ||||
−0.847767 | + | 0.530368i | \(0.822054\pi\) | |||||||
\(440\) | 614154. | + | 1.43670e6i | 0.151233 | + | 0.353780i | ||||
\(441\) | 48262.8 | − | 4.02136e6i | 0.0118172 | − | 0.984638i | ||||
\(442\) | −810188. | + | 810188.i | −0.197256 | + | 0.197256i | ||||
\(443\) | −1.99417e6 | + | 1.99417e6i | −0.482784 | + | 0.482784i | −0.906020 | − | 0.423235i | \(-0.860894\pi\) |
0.423235 | + | 0.906020i | \(0.360894\pi\) | |||||||
\(444\) | −1.12839e6 | + | 1.11493e6i | −0.271646 | + | 0.268406i | ||||
\(445\) | −5.50109e6 | − | 2.20634e6i | −1.31689 | − | 0.528169i | ||||
\(446\) | 572435.i | 0.136266i | ||||||||
\(447\) | 33461.2 | − | 5.57632e6i | 0.00792087 | − | 1.32002i | ||||
\(448\) | −267913. | − | 267913.i | −0.0630666 | − | 0.0630666i | ||||
\(449\) | 524045. | 0.122674 | 0.0613370 | − | 0.998117i | \(-0.480464\pi\) | ||||
0.0613370 | + | 0.998117i | \(0.480464\pi\) | |||||||
\(450\) | −9952.75 | − | 944860.i | −0.00231692 | − | 0.219956i | ||||
\(451\) | 2.31455e6 | 0.535827 | ||||||||
\(452\) | −4.14691e6 | − | 4.14691e6i | −0.954725 | − | 0.954725i | ||||
\(453\) | 16933.5 | − | 2.82198e6i | 0.00387706 | − | 0.646113i | ||||
\(454\) | − | 126349.i | − | 0.0287694i | ||||||
\(455\) | −435229. | − | 174559.i | −0.0985574 | − | 0.0395288i | ||||
\(456\) | −1.72773e6 | + | 1.70712e6i | −0.389103 | + | 0.384461i | ||||
\(457\) | −782574. | + | 782574.i | −0.175281 | + | 0.175281i | −0.789295 | − | 0.614014i | \(-0.789554\pi\) |
0.614014 | + | 0.789295i | \(0.289554\pi\) | |||||||
\(458\) | −245200. | + | 245200.i | −0.0546206 | + | 0.0546206i | ||||
\(459\) | −4.79749e6 | + | 4.62780e6i | −1.06287 | + | 1.02528i | ||||
\(460\) | −231920. | − | 542534.i | −0.0511027 | − | 0.119545i | ||||
\(461\) | 1.72240e6i | 0.377469i | 0.982028 | + | 0.188734i | \(0.0604385\pi\) | ||||
−0.982028 | + | 0.188734i | \(0.939562\pi\) | |||||||
\(462\) | −111839. | − | 671.100i | −0.0243775 | − | 0.000146279i | ||||
\(463\) | 4.87630e6 | + | 4.87630e6i | 1.05715 | + | 1.05715i | 0.998265 | + | 0.0588893i | \(0.0187559\pi\) |
0.0588893 | + | 0.998265i | \(0.481244\pi\) | |||||||
\(464\) | 6.19414e6 | 1.33563 | ||||||||
\(465\) | −998425. | + | 2.44678e6i | −0.214133 | + | 0.524762i | ||||
\(466\) | 126068. | 0.0268931 | ||||||||
\(467\) | 5.35029e6 | + | 5.35029e6i | 1.13523 | + | 1.13523i | 0.989294 | + | 0.145940i | \(0.0466205\pi\) |
0.145940 | + | 0.989294i | \(0.453380\pi\) | |||||||
\(468\) | −2.77062e6 | + | 2.70490e6i | −0.584739 | + | 0.570870i | ||||
\(469\) | 918938.i | 0.192910i | ||||||||
\(470\) | −54667.5 | + | 136303.i | −0.0114152 | + | 0.0284616i | ||||
\(471\) | −2.94635e6 | − | 2.98193e6i | −0.611973 | − | 0.619362i | ||||
\(472\) | 1.16744e6 | − | 1.16744e6i | 0.241201 | − | 0.241201i | ||||
\(473\) | 3.49561e6 | − | 3.49561e6i | 0.718406 | − | 0.718406i | ||||
\(474\) | −407624. | − | 412546.i | −0.0833325 | − | 0.0843386i | ||||
\(475\) | 4.32956e6 | − | 4.52922e6i | 0.880460 | − | 0.921063i | ||||
\(476\) | 859031.i | 0.173777i | ||||||||
\(477\) | 4.60581e6 | − | 4.49656e6i | 0.926850 | − | 0.904867i | ||||
\(478\) | −950808. | − | 950808.i | −0.190337 | − | 0.190337i | ||||
\(479\) | 2.68281e6 | 0.534257 | 0.267129 | − | 0.963661i | \(-0.413925\pi\) | ||||
0.267129 | + | 0.963661i | \(0.413925\pi\) | |||||||
\(480\) | −2.87504e6 | + | 1.20866e6i | −0.569563 | + | 0.239443i | ||||
\(481\) | 1.74862e6 | 0.344615 | ||||||||
\(482\) | −301242. | − | 301242.i | −0.0590606 | − | 0.0590606i | ||||
\(483\) | 86614.0 | + | 519.735i | 0.0168935 | + | 0.000101371i | ||||
\(484\) | − | 964947.i | − | 0.187236i | ||||||
\(485\) | −2.40926e6 | + | 1.02990e6i | −0.465082 | + | 0.198812i | ||||
\(486\) | 833840. | − | 785248.i | 0.160137 | − | 0.150805i | ||||
\(487\) | −4.62946e6 | + | 4.62946e6i | −0.884521 | + | 0.884521i | −0.993990 | − | 0.109469i | \(-0.965085\pi\) |
0.109469 | + | 0.993990i | \(0.465085\pi\) | |||||||
\(488\) | −38011.0 | + | 38011.0i | −0.00722537 | + | 0.00722537i | ||||
\(489\) | 5.94817e6 | − | 5.87721e6i | 1.12489 | − | 1.11147i | ||||
\(490\) | −1.05856e6 | + | 452508.i | −0.199170 | + | 0.0851405i | ||||
\(491\) | − | 5.60483e6i | − | 1.04920i | −0.851349 | − | 0.524600i | \(-0.824215\pi\) | ||
0.851349 | − | 0.524600i | \(-0.175785\pi\) | |||||||
\(492\) | −18329.9 | + | 3.05469e6i | −0.00341388 | + | 0.568924i | ||||
\(493\) | −8.78078e6 | − | 8.78078e6i | −1.62710 | − | 1.62710i | ||||
\(494\) | 1.30551e6 | 0.240692 | ||||||||
\(495\) | 1.87303e6 | − | 4.51253e6i | 0.343583 | − | 0.827764i | ||||
\(496\) | 2.66186e6 | 0.485826 | ||||||||
\(497\) | −95783.3 | − | 95783.3i | −0.0173940 | − | 0.0173940i | ||||
\(498\) | −5048.21 | + | 841286.i | −0.000912146 | + | 0.152009i | ||||
\(499\) | − | 4.52825e6i | − | 0.814103i | −0.913405 | − | 0.407052i | \(-0.866557\pi\) | ||
0.913405 | − | 0.407052i | \(-0.133443\pi\) | |||||||
\(500\) | 4.84314e6 | − | 2.20069e6i | 0.866367 | − | 0.393671i | ||||
\(501\) | −3.32650e6 | + | 3.28681e6i | −0.592097 | + | 0.585033i | ||||
\(502\) | 172270. | − | 172270.i | 0.0305105 | − | 0.0305105i | ||||
\(503\) | −6.67659e6 | + | 6.67659e6i | −1.17662 | + | 1.17662i | −0.196015 | + | 0.980601i | \(0.562800\pi\) |
−0.980601 | + | 0.196015i | \(0.937200\pi\) | |||||||
\(504\) | 3632.88 | − | 302700.i | 0.000637052 | − | 0.0530806i | ||||
\(505\) | −285895. | + | 712824.i | −0.0498859 | + | 0.124381i | ||||
\(506\) | 155123.i | 0.0269339i | ||||||||
\(507\) | −1.51958e6 | − | 9118.35i | −0.262544 | − | 0.00157542i | ||||
\(508\) | 2.14784e6 | + | 2.14784e6i | 0.369269 | + | 0.369269i | ||||
\(509\) | −5.52619e6 | −0.945434 | −0.472717 | − | 0.881214i | \(-0.656727\pi\) | ||||
−0.472717 | + | 0.881214i | \(0.656727\pi\) | |||||||
\(510\) | 1.76669e6 | + | 720908.i | 0.300770 | + | 0.122731i | ||||
\(511\) | 264298. | 0.0447756 | ||||||||
\(512\) | 3.76477e6 | + | 3.76477e6i | 0.634692 | + | 0.634692i | ||||
\(513\) | 7.59378e6 | + | 136715.i | 1.27399 | + | 0.0229362i | ||||
\(514\) | − | 1.08087e6i | − | 0.180454i | ||||||
\(515\) | −1.41129e6 | − | 3.30144e6i | −0.234475 | − | 0.548510i | ||||
\(516\) | 4.58574e6 | + | 4.64111e6i | 0.758203 | + | 0.767357i | ||||
\(517\) | −536938. | + | 536938.i | −0.0883483 | + | 0.0883483i | ||||
\(518\) | −47135.7 | + | 47135.7i | −0.00771836 | + | 0.00771836i | ||||
\(519\) | −816791. | − | 826653.i | −0.133104 | − | 0.134712i | ||||
\(520\) | 2.10979e6 | + | 846182.i | 0.342161 | + | 0.137232i | ||||
\(521\) | − | 619733.i | − | 0.100025i | −0.998749 | − | 0.0500127i | \(-0.984074\pi\) | ||
0.998749 | − | 0.0500127i | \(-0.0159262\pi\) | |||||||
\(522\) | 1.49059e6 | + | 1.52681e6i | 0.239432 | + | 0.245249i | ||||
\(523\) | 6.44079e6 | + | 6.44079e6i | 1.02964 | + | 1.02964i | 0.999547 | + | 0.0300909i | \(0.00957968\pi\) |
0.0300909 | + | 0.999547i | \(0.490420\pi\) | |||||||
\(524\) | −9.52584e6 | −1.51557 | ||||||||
\(525\) | 12911.0 | + | 780821.i | 0.00204439 | + | 0.123638i | ||||
\(526\) | 701596. | 0.110566 | ||||||||
\(527\) | −3.77343e6 | − | 3.77343e6i | −0.591848 | − | 0.591848i | ||||
\(528\) | −4.92124e6 | − | 29530.3i | −0.768227 | − | 0.00460981i | ||||
\(529\) | 6.31621e6i | 0.981335i | ||||||||
\(530\) | −1.71015e6 | − | 685897.i | −0.264451 | − | 0.106064i | ||||
\(531\) | −5.16232e6 | − | 61956.1i | −0.794527 | − | 0.00953560i | ||||
\(532\) | 692106. | − | 692106.i | 0.106021 | − | 0.106021i | ||||
\(533\) | 2.38106e6 | − | 2.38106e6i | 0.363039 | − | 0.363039i | ||||
\(534\) | −1.46294e6 | + | 1.44549e6i | −0.222011 | + | 0.219362i | ||||
\(535\) | 1.46775e6 | + | 3.43353e6i | 0.221701 | + | 0.518629i | ||||
\(536\) | − | 4.45459e6i | − | 0.669723i | ||||||
\(537\) | −49050.9 | + | 8.17435e6i | −0.00734026 | + | 1.22326i | ||||
\(538\) | 1.13733e6 | + | 1.13733e6i | 0.169408 | + | 0.169408i | ||||
\(539\) | −5.95256e6 | −0.882534 | ||||||||
\(540\) | 5.94070e6 | + | 2.50772e6i | 0.876704 | + | 0.370079i | ||||
\(541\) | −8.91778e6 | −1.30998 | −0.654988 | − | 0.755639i | \(-0.727326\pi\) | ||||
−0.654988 | + | 0.755639i | \(0.727326\pi\) | |||||||
\(542\) | −691237. | − | 691237.i | −0.101072 | − | 0.101072i | ||||
\(543\) | 15339.4 | − | 2.55631e6i | 0.00223259 | − | 0.372062i | ||||
\(544\) | − | 6.29790e6i | − | 0.912428i | ||||||
\(545\) | 1.20193e6 | − | 2.99677e6i | 0.173335 | − | 0.432178i | ||||
\(546\) | −115743. | + | 114363.i | −0.0166156 | + | 0.0164173i | ||||
\(547\) | −4.50080e6 | + | 4.50080e6i | −0.643164 | + | 0.643164i | −0.951332 | − | 0.308168i | \(-0.900284\pi\) |
0.308168 | + | 0.951332i | \(0.400284\pi\) | |||||||
\(548\) | 1.34449e6 | − | 1.34449e6i | 0.191252 | − | 0.191252i | ||||
\(549\) | 168082. | + | 2017.25i | 0.0238007 | + | 0.000285647i | ||||
\(550\) | −1.39824e6 | + | 31513.5i | −0.197094 | + | 0.00444211i | ||||
\(551\) | 1.41490e7i | 1.98540i | ||||||||
\(552\) | −419865. | − | 2519.43i | −0.0586491 | − | 0.000351929i | ||||
\(553\) | 338923. | + | 338923.i | 0.0471290 | + | 0.0471290i | ||||
\(554\) | 2.73195e6 | 0.378180 | ||||||||
\(555\) | −1.12855e6 | − | 2.68448e6i | −0.155521 | − | 0.369937i | ||||
\(556\) | 316033. | 0.0433556 | ||||||||
\(557\) | −6.79813e6 | − | 6.79813e6i | −0.928435 | − | 0.928435i | 0.0691698 | − | 0.997605i | \(-0.477965\pi\) |
−0.997605 | + | 0.0691698i | \(0.977965\pi\) | |||||||
\(558\) | 640564. | + | 656126.i | 0.0870917 | + | 0.0892076i | ||||
\(559\) | − | 7.19213e6i | − | 0.973482i | ||||||
\(560\) | 723290. | − | 309189.i | 0.0974636 | − | 0.0416634i | ||||
\(561\) | 6.93445e6 | + | 7.01818e6i | 0.930261 | + | 0.941493i | ||||
\(562\) | 1.09911e6 | − | 1.09911e6i | 0.146792 | − | 0.146792i | ||||
\(563\) | 9.18684e6 | − | 9.18684e6i | 1.22150 | − | 1.22150i | 0.254408 | − | 0.967097i | \(-0.418120\pi\) |
0.967097 | − | 0.254408i | \(-0.0818804\pi\) | |||||||
\(564\) | −704387. | − | 712891.i | −0.0932424 | − | 0.0943682i | ||||
\(565\) | 9.89942e6 | − | 4.23177e6i | 1.30463 | − | 0.557700i | ||||
\(566\) | 992593.i | 0.130236i | ||||||||
\(567\) | −685225. | + | 653096.i | −0.0895108 | + | 0.0853138i | ||||
\(568\) | 464313. | + | 464313.i | 0.0603866 | + | 0.0603866i | ||||
\(569\) | −3.22815e6 | −0.417996 | −0.208998 | − | 0.977916i | \(-0.567020\pi\) | ||||
−0.208998 | + | 0.977916i | \(0.567020\pi\) | |||||||
\(570\) | −842565. | − | 2.00421e6i | −0.108622 | − | 0.258378i | ||||
\(571\) | −9.43358e6 | −1.21084 | −0.605420 | − | 0.795907i | \(-0.706995\pi\) | ||||
−0.605420 | + | 0.795907i | \(0.706995\pi\) | |||||||
\(572\) | 4.05253e6 | + | 4.05253e6i | 0.517888 | + | 0.517888i | ||||
\(573\) | 8.71634e6 | + | 52303.2i | 1.10904 | + | 0.00665490i | ||||
\(574\) | 128367.i | 0.0162620i | ||||||||
\(575\) | 1.08287e6 | − | 24405.7i | 0.136586 | − | 0.00307837i | ||||
\(576\) | 68923.3 | − | 5.74284e6i | 0.00865585 | − | 0.721224i | ||||
\(577\) | 9.98594e6 | − | 9.98594e6i | 1.24868 | − | 1.24868i | 0.292370 | − | 0.956305i | \(-0.405556\pi\) |
0.956305 | − | 0.292370i | \(-0.0944438\pi\) | |||||||
\(578\) | −1.47529e6 | + | 1.47529e6i | −0.183679 | + | 0.183679i | ||||
\(579\) | 2.35246e6 | − | 2.32439e6i | 0.291625 | − | 0.288146i | ||||
\(580\) | −4.47175e6 | + | 1.11494e7i | −0.551960 | + | 1.37621i | ||||
\(581\) | − | 695298.i | − | 0.0854537i | ||||||
\(582\) | −5455.41 | + | 909146.i | −0.000667606 | + | 0.111257i | ||||
\(583\) | −6.73682e6 | − | 6.73682e6i | −0.820887 | − | 0.820887i | ||||
\(584\) | −1.28119e6 | −0.155447 | ||||||||
\(585\) | −2.71535e6 | − | 6.56906e6i | −0.328047 | − | 0.793622i | ||||
\(586\) | −3.47193e6 | −0.417663 | ||||||||
\(587\) | 1.08667e7 | + | 1.08667e7i | 1.30168 | + | 1.30168i | 0.927260 | + | 0.374419i | \(0.122158\pi\) |
0.374419 | + | 0.927260i | \(0.377842\pi\) | |||||||
\(588\) | 47140.9 | − | 7.85605e6i | 0.00562283 | − | 0.937046i | ||||
\(589\) | 6.08037e6i | 0.722174i | ||||||||
\(590\) | 580896. | + | 1.35890e6i | 0.0687018 | + | 0.160715i | ||||
\(591\) | 3.71673e6 | − | 3.67239e6i | 0.437716 | − | 0.432494i | ||||
\(592\) | −2.07410e6 | + | 2.07410e6i | −0.243235 | + | 0.243235i | ||||
\(593\) | −6.83953e6 | + | 6.83953e6i | −0.798710 | + | 0.798710i | −0.982892 | − | 0.184182i | \(-0.941036\pi\) |
0.184182 | + | 0.982892i | \(0.441036\pi\) | |||||||
\(594\) | −1.17699e6 | − | 1.22015e6i | −0.136870 | − | 0.141889i | ||||
\(595\) | −1.46364e6 | − | 587027.i | −0.169489 | − | 0.0679775i | ||||
\(596\) | − | 1.08934e7i | − | 1.25617i | ||||||
\(597\) | −9.38928e6 | − | 56341.2i | −1.07819 | − | 0.00646979i | ||||
\(598\) | 159581. | + | 159581.i | 0.0182485 | + | 0.0182485i | ||||
\(599\) | 1.22951e7 | 1.40012 | 0.700060 | − | 0.714084i | \(-0.253156\pi\) | ||||
0.700060 | + | 0.714084i | \(0.253156\pi\) | |||||||
\(600\) | −62586.8 | − | 3.78506e6i | −0.00709748 | − | 0.429235i | ||||
\(601\) | 5.35161e6 | 0.604364 | 0.302182 | − | 0.953250i | \(-0.402285\pi\) | ||||
0.302182 | + | 0.953250i | \(0.402285\pi\) | |||||||
\(602\) | 193870. | + | 193870.i | 0.0218032 | + | 0.0218032i | ||||
\(603\) | −9.96711e6 | + | 9.73071e6i | −1.11629 | + | 1.08981i | ||||
\(604\) | − | 5.51276e6i | − | 0.614861i | ||||||
\(605\) | 1.64410e6 | + | 659405.i | 0.182616 | + | 0.0732426i | ||||
\(606\) | 187305. | + | 189566.i | 0.0207189 | + | 0.0209691i | ||||
\(607\) | 1.03013e7 | − | 1.03013e7i | 1.13480 | − | 1.13480i | 0.145433 | − | 0.989368i | \(-0.453542\pi\) |
0.989368 | − | 0.145433i | \(-0.0464576\pi\) | |||||||
\(608\) | −5.07411e6 | + | 5.07411e6i | −0.556674 | + | 0.556674i | ||||
\(609\) | −1.23946e6 | − | 1.25442e6i | −0.135422 | − | 0.137057i | ||||
\(610\) | −18913.6 | − | 44244.8i | −0.00205802 | − | 0.00481435i | ||||
\(611\) | 1.10474e6i | 0.119717i | ||||||||
\(612\) | −9.31735e6 | + | 9.09636e6i | −1.00557 | + | 0.981723i | ||||
\(613\) | 4.89015e6 | + | 4.89015e6i | 0.525619 | + | 0.525619i | 0.919263 | − | 0.393644i | \(-0.128786\pi\) |
−0.393644 | + | 0.919263i | \(0.628786\pi\) | |||||||
\(614\) | 1.25303e6 | 0.134134 | ||||||||
\(615\) | −5.19212e6 | − | 2.11868e6i | −0.553550 | − | 0.225880i | ||||
\(616\) | −448066. | −0.0475763 | ||||||||
\(617\) | −833237. | − | 833237.i | −0.0881162 | − | 0.0881162i | 0.661675 | − | 0.749791i | \(-0.269846\pi\) |
−0.749791 | + | 0.661675i | \(0.769846\pi\) | |||||||
\(618\) | −1.24581e6 | − | 7475.60i | −0.131214 | − | 0.000787363i | ||||
\(619\) | 1.53788e7i | 1.61323i | 0.591076 | + | 0.806616i | \(0.298703\pi\) | ||||
−0.591076 | + | 0.806616i | \(0.701297\pi\) | |||||||
\(620\) | −1.92168e6 | + | 4.79134e6i | −0.200772 | + | 0.500585i | ||||
\(621\) | 911525. | + | 944948.i | 0.0948505 | + | 0.0983284i | ||||
\(622\) | −705358. | + | 705358.i | −0.0731027 | + | 0.0731027i | ||||
\(623\) | 1.20187e6 | − | 1.20187e6i | 0.124061 | − | 0.124061i | ||||
\(624\) | −5.09304e6 | + | 5.03228e6i | −0.523619 | + | 0.517373i | ||||
\(625\) | 439972. | + | 9.75571e6i | 0.0450532 | + | 0.998985i | ||||
\(626\) | − | 2.39999e6i | − | 0.244779i | ||||||
\(627\) | 67454.9 | − | 1.12414e7i | 0.00685243 | − | 1.14196i | ||||
\(628\) | −5.79047e6 | − | 5.79047e6i | −0.585888 | − | 0.585888i | ||||
\(629\) | 5.88047e6 | 0.592632 | ||||||||
\(630\) | 250269. | + | 103880.i | 0.0251221 | + | 0.0104275i | ||||
\(631\) | 6.50224e6 | 0.650114 | 0.325057 | − | 0.945694i | \(-0.394617\pi\) | ||||
0.325057 | + | 0.945694i | \(0.394617\pi\) | |||||||
\(632\) | −1.64294e6 | − | 1.64294e6i | −0.163618 | − | 0.163618i | ||||
\(633\) | −84668.6 | + | 1.41101e7i | −0.00839872 | + | 1.39965i | ||||
\(634\) | 2.54372e6i | 0.251331i | ||||||||
\(635\) | −5.12728e6 | + | 2.19179e6i | −0.504606 | + | 0.215707i | ||||
\(636\) | 8.94445e6 | − | 8.83775e6i | 0.876821 | − | 0.866361i | ||||
\(637\) | −6.12362e6 | + | 6.12362e6i | −0.597943 | + | 0.597943i | ||||
\(638\) | 2.23323e6 | − | 2.23323e6i | 0.217211 | − | 0.217211i | ||||
\(639\) | 24641.2 | − | 2.05316e6i | 0.00238731 | − | 0.198916i | ||||
\(640\) | −7.39861e6 | + | 3.16273e6i | −0.714003 | + | 0.305219i | ||||
\(641\) | 3.82299e6i | 0.367501i | 0.982973 | + | 0.183750i | \(0.0588238\pi\) | ||||
−0.982973 | + | 0.183750i | \(0.941176\pi\) | |||||||
\(642\) | 1.29566e6 | + | 7774.71i | 0.124066 | + | 0.000744469i | ||||
\(643\) | −7.11939e6 | − | 7.11939e6i | −0.679071 | − | 0.679071i | 0.280719 | − | 0.959790i | \(-0.409427\pi\) |
−0.959790 | + | 0.280719i | \(0.909427\pi\) | |||||||
\(644\) | 169201. | 0.0160764 | ||||||||
\(645\) | −1.10413e7 | + | 4.64175e6i | −1.04501 | + | 0.439321i | ||||
\(646\) | 4.39031e6 | 0.413917 | ||||||||
\(647\) | −6.21104e6 | − | 6.21104e6i | −0.583316 | − | 0.583316i | 0.352497 | − | 0.935813i | \(-0.385333\pi\) |
−0.935813 | + | 0.352497i | \(0.885333\pi\) | |||||||
\(648\) | 3.32165e6 | − | 3.16591e6i | 0.310754 | − | 0.296184i | ||||
\(649\) | 7.64144e6i | 0.712137i | ||||||||
\(650\) | −1.40600e6 | + | 1.47084e6i | −0.130527 | + | 0.136547i | ||||
\(651\) | −532642. | − | 539073.i | −0.0492587 | − | 0.0498534i | ||||
\(652\) | 1.15505e7 | − | 1.15505e7i | 1.06410 | − | 1.06410i | ||||
\(653\) | 752240. | − | 752240.i | 0.0690356 | − | 0.0690356i | −0.671746 | − | 0.740782i | \(-0.734455\pi\) |
0.740782 | + | 0.671746i | \(0.234455\pi\) | |||||||
\(654\) | −787445. | − | 796952.i | −0.0719906 | − | 0.0728598i | ||||
\(655\) | 6.50957e6 | − | 1.62303e7i | 0.592855 | − | 1.47817i | ||||
\(656\) | 5.64852e6i | 0.512478i | ||||||||
\(657\) | 2.79867e6 | + | 2.86666e6i | 0.252952 | + | 0.259097i | ||||
\(658\) | −29779.1 | − | 29779.1i | −0.00268131 | − | 0.00268131i | ||||
\(659\) | 1.49063e7 | 1.33707 | 0.668536 | − | 0.743679i | \(-0.266921\pi\) | ||||
0.668536 | + | 0.743679i | \(0.266921\pi\) | |||||||
\(660\) | 3.60596e6 | − | 8.83690e6i | 0.322226 | − | 0.789660i | ||||
\(661\) | −1.55144e7 | −1.38112 | −0.690558 | − | 0.723277i | \(-0.742635\pi\) | ||||
−0.690558 | + | 0.723277i | \(0.742635\pi\) | |||||||
\(662\) | −147463. | − | 147463.i | −0.0130779 | − | 0.0130779i | ||||
\(663\) | 1.43536e7 | + | 86130.0i | 1.26817 | + | 0.00760976i | ||||
\(664\) | 3.37048e6i | 0.296669i | ||||||||
\(665\) | 706269. | + | 1.65218e6i | 0.0619321 | + | 0.144878i | ||||
\(666\) | −1.01037e6 | − | 12126.1i | −0.0882666 | − | 0.00105934i | ||||
\(667\) | −1.72953e6 | + | 1.72953e6i | −0.150526 | + | 0.150526i | ||||
\(668\) | −6.45958e6 | + | 6.45958e6i | −0.560097 | + | 0.560097i | ||||
\(669\) | 5.10116e6 | − | 5.04031e6i | 0.440660 | − | 0.435403i | ||||
\(670\) | 3.70082e6 | + | 1.48430e6i | 0.318501 | + | 0.127743i | ||||
\(671\) | − | 248800.i | − | 0.0213326i | ||||||
\(672\) | 5366.64 | − | 894352.i | 0.000458437 | − | 0.0763986i | ||||
\(673\) | −9.88243e6 | − | 9.88243e6i | −0.841058 | − | 0.841058i | 0.147938 | − | 0.988997i | \(-0.452736\pi\) |
−0.988997 | + | 0.147938i | \(0.952736\pi\) | |||||||
\(674\) | −1.01836e6 | −0.0863475 | ||||||||
\(675\) | −8.33234e6 | + | 8.40822e6i | −0.703894 | + | 0.710305i | ||||
\(676\) | −2.96851e6 | −0.249845 | ||||||||
\(677\) | −9.07764e6 | − | 9.07764e6i | −0.761204 | − | 0.761204i | 0.215336 | − | 0.976540i | \(-0.430915\pi\) |
−0.976540 | + | 0.215336i | \(0.930915\pi\) | |||||||
\(678\) | 22415.7 | − | 3.73559e6i | 0.00187274 | − | 0.312094i | ||||
\(679\) | − | 751382.i | − | 0.0625441i | ||||||
\(680\) | 7.09503e6 | + | 2.84563e6i | 0.588413 | + | 0.235997i | ||||
\(681\) | −1.12594e6 | + | 1.11250e6i | −0.0930349 | + | 0.0919250i | ||||
\(682\) | 959702. | − | 959702.i | 0.0790088 | − | 0.0790088i | ||||
\(683\) | 1.17688e7 | − | 1.17688e7i | 0.965341 | − | 0.965341i | −0.0340786 | − | 0.999419i | \(-0.510850\pi\) |
0.999419 | + | 0.0340786i | \(0.0108496\pi\) | |||||||
\(684\) | 1.48356e7 | + | 178051.i | 1.21245 | + | 0.0145514i | ||||
\(685\) | 1.37200e6 | + | 3.20954e6i | 0.111719 | + | 0.261347i | ||||
\(686\) | − | 665396.i | − | 0.0539846i | ||||||
\(687\) | 4.34405e6 | + | 26066.9i | 0.351159 | + | 0.00210716i | ||||
\(688\) | 8.53083e6 | + | 8.53083e6i | 0.687100 | + | 0.687100i | ||||
\(689\) | −1.38608e7 | −1.11235 | ||||||||
\(690\) | 141995. | − | 347980.i | 0.0113541 | − | 0.0278247i | ||||
\(691\) | 1.13832e7 | 0.906920 | 0.453460 | − | 0.891277i | \(-0.350189\pi\) | ||||
0.453460 | + | 0.891277i | \(0.350189\pi\) | |||||||
\(692\) | −1.60524e6 | − | 1.60524e6i | −0.127431 | − | 0.127431i | ||||
\(693\) | 978767. | + | 1.00255e6i | 0.0774188 | + | 0.0792996i | ||||
\(694\) | − | 97533.0i | − | 0.00768693i | ||||||
\(695\) | −215964. | + | 538463.i | −0.0169597 | + | 0.0422858i | ||||
\(696\) | 6.00832e6 | + | 6.08086e6i | 0.470143 | + | 0.475819i | ||||
\(697\) | 8.00730e6 | − | 8.00730e6i | 0.624316 | − | 0.624316i | ||||
\(698\) | −1.02754e6 | + | 1.02754e6i | −0.0798290 | + | 0.0798290i | ||||
\(699\) | −1.11004e6 | − | 1.12344e6i | −0.0859300 | − | 0.0869674i | ||||
\(700\) | 34373.5 | + | 1.52514e6i | 0.00265142 | + | 0.117642i | ||||
\(701\) | − | 1.43910e7i | − | 1.10611i | −0.833146 | − | 0.553053i | \(-0.813463\pi\) | ||
0.833146 | − | 0.553053i | \(-0.186537\pi\) | |||||||
\(702\) | −2.46604e6 | − | 44397.2i | −0.188867 | − | 0.00340027i | ||||
\(703\) | −4.73779e6 | − | 4.73779e6i | −0.361566 | − | 0.361566i | ||||
\(704\) | −8.50074e6 | −0.646436 | ||||||||
\(705\) | 1.69599e6 | − | 712989.i | 0.128514 | − | 0.0540269i | ||||
\(706\) | −400530. | −0.0302429 | ||||||||
\(707\) | −155736. | − | 155736.i | −0.0117177 | − | 0.0117177i | ||||
\(708\) | −1.00850e7 | − | 60515.9i | −0.756123 | − | 0.00453719i | ||||
\(709\) | 3.32746e6i | 0.248598i | 0.992245 | + | 0.124299i | \(0.0396681\pi\) | ||||
−0.992245 | + | 0.124299i | \(0.960332\pi\) | |||||||
\(710\) | −540460. | + | 231034.i | −0.0402362 | + | 0.0172000i | ||||
\(711\) | −87191.2 | + | 7.26496e6i | −0.00646843 | + | 0.538963i | ||||
\(712\) | −5.82609e6 | + | 5.82609e6i | −0.430703 | + | 0.430703i | ||||
\(713\) | −743243. | + | 743243.i | −0.0547529 | + | 0.0547529i | ||||
\(714\) | −389235. | + | 384592.i | −0.0285737 | + | 0.0282328i | ||||
\(715\) | −9.67412e6 | + | 4.13546e6i | −0.707695 | + | 0.302523i | ||||
\(716\) | 1.59687e7i | 1.16409i | ||||||||
\(717\) | −101079. | + | 1.68449e7i | −0.00734283 | + | 1.22369i | ||||
\(718\) | −2.66746e6 | − | 2.66746e6i | −0.193102 | − | 0.193102i | ||||
\(719\) | −4.31981e6 | −0.311632 | −0.155816 | − | 0.987786i | \(-0.549801\pi\) | ||||
−0.155816 | + | 0.987786i | \(0.549801\pi\) | |||||||
\(720\) | 1.10126e7 | + | 4.57102e6i | 0.791693 | + | 0.328611i | ||||
\(721\) | 1.02963e6 | 0.0737635 | ||||||||
\(722\) | −1.35854e6 | − | 1.35854e6i | −0.0969903 | − | 0.0969903i | ||||
\(723\) | −32024.6 | + | 5.33692e6i | −0.00227845 | + | 0.379704i | ||||
\(724\) | − | 4.99378e6i | − | 0.354065i | ||||||
\(725\) | −1.59409e7 | − | 1.52381e7i | −1.12633 | − | 1.07668i | ||||
\(726\) | 437226. | − | 432011.i | 0.0307868 | − | 0.0304195i | ||||
\(727\) | −1.03718e7 | + | 1.03718e7i | −0.727811 | + | 0.727811i | −0.970183 | − | 0.242373i | \(-0.922074\pi\) |
0.242373 | + | 0.970183i | \(0.422074\pi\) | |||||||
\(728\) | −460943. | + | 460943.i | −0.0322343 | + | 0.0322343i | ||||
\(729\) | −1.43396e7 | − | 516494.i | −0.999352 | − | 0.0359953i | ||||
\(730\) | 426904. | − | 1.06440e6i | 0.0296499 | − | 0.0739262i | ||||
\(731\) | − | 2.41865e7i | − | 1.67409i | ||||||
\(732\) | 328361. | + | 1970.36i | 0.0226503 | + | 0.000135915i | ||||
\(733\) | 6.93586e6 | + | 6.93586e6i | 0.476804 | + | 0.476804i | 0.904108 | − | 0.427304i | \(-0.140537\pi\) |
−0.427304 | + | 0.904108i | \(0.640537\pi\) | |||||||
\(734\) | −5.51902e6 | −0.378113 | ||||||||
\(735\) | 1.33531e7 | + | 5.44882e6i | 0.911725 | + | 0.372035i | ||||
\(736\) | −1.24048e6 | −0.0844104 | ||||||||
\(737\) | 1.45787e7 | + | 1.45787e7i | 0.988666 | + | 0.988666i | ||||
\(738\) | −1.39231e6 | + | 1.35929e6i | −0.0941015 | + | 0.0918695i | ||||
\(739\) | − | 5.27869e6i | − | 0.355562i | −0.984070 | − | 0.177781i | \(-0.943108\pi\) | ||
0.984070 | − | 0.177781i | \(-0.0568919\pi\) | |||||||
\(740\) | −2.23602e6 | − | 5.23074e6i | −0.150105 | − | 0.351143i | ||||
\(741\) | −1.14950e7 | − | 1.16338e7i | −0.769068 | − | 0.778354i | ||||
\(742\) | 373631. | − | 373631.i | 0.0249134 | − | 0.0249134i | ||||
\(743\) | −1.42934e7 | + | 1.42934e7i | −0.949871 | + | 0.949871i | −0.998802 | − | 0.0489311i | \(-0.984419\pi\) |
0.0489311 | + | 0.998802i | \(0.484419\pi\) | |||||||
\(744\) | 2.58200e6 | + | 2.61318e6i | 0.171011 | + | 0.173076i | ||||
\(745\) | 1.85604e7 | + | 7.44410e6i | 1.22517 | + | 0.491384i | ||||
\(746\) | 5.45518e6i | 0.358891i | ||||||||
\(747\) | 7.54144e6 | − | 7.36257e6i | 0.494485 | − | 0.482756i | ||||
\(748\) | 1.36283e7 | + | 1.36283e7i | 0.890610 | + | 0.890610i | ||||
\(749\) | −1.07082e6 | −0.0697450 | ||||||||
\(750\) | 3.16544e6 | + | 1.20922e6i | 0.205486 | + | 0.0784967i | ||||
\(751\) | −4.87198e6 | −0.315214 | −0.157607 | − | 0.987502i | \(-0.550378\pi\) | ||||
−0.157607 | + | 0.987502i | \(0.550378\pi\) | |||||||
\(752\) | −1.31037e6 | − | 1.31037e6i | −0.0844983 | − | 0.0844983i | ||||
\(753\) | −3.05200e6 | − | 18313.8i | −0.196154 | − | 0.00117704i | ||||
\(754\) | − | 4.59481e6i | − | 0.294333i | ||||||
\(755\) | 9.39277e6 | + | 3.76719e6i | 0.599689 | + | 0.240520i | ||||
\(756\) | −1.33089e6 | + | 1.28382e6i | −0.0846910 | + | 0.0816955i | ||||
\(757\) | −4.56529e6 | + | 4.56529e6i | −0.289554 | + | 0.289554i | −0.836904 | − | 0.547350i | \(-0.815637\pi\) |
0.547350 | + | 0.836904i | \(0.315637\pi\) | |||||||
\(758\) | 3.31406e6 | − | 3.31406e6i | 0.209501 | − | 0.209501i | ||||
\(759\) | 1.38235e6 | − | 1.36586e6i | 0.0870992 | − | 0.0860601i | ||||
\(760\) | −3.42367e6 | − | 8.00902e6i | −0.215009 | − | 0.502974i | ||||
\(761\) | 2.03979e7i | 1.27680i | 0.769703 | + | 0.638402i | \(0.220404\pi\) | ||||
−0.769703 | + | 0.638402i | \(0.779596\pi\) | |||||||
\(762\) | −11609.9 | + | 1.93480e6i | −0.000724341 | + | 0.120712i | ||||
\(763\) | 654729. | + | 654729.i | 0.0407146 | + | 0.0407146i | ||||
\(764\) | 1.70275e7 | 1.05540 | ||||||||
\(765\) | −9.13148e6 | − | 2.20912e7i | −0.564141 | − | 1.36479i | ||||
\(766\) | −1.81260e6 | −0.111617 | ||||||||
\(767\) | 7.86103e6 | + | 7.86103e6i | 0.482493 | + | 0.482493i | ||||
\(768\) | 53991.2 | − | 8.99764e6i | 0.00330308 | − | 0.550460i | ||||
\(769\) | − | 2.14987e7i | − | 1.31098i | −0.755203 | − | 0.655490i | \(-0.772462\pi\) | ||
0.755203 | − | 0.655490i | \(-0.227538\pi\) | |||||||
\(770\) | 149299. | − | 372249.i | 0.00907468 | − | 0.0226259i | ||||
\(771\) | −9.63204e6 | + | 9.51713e6i | −0.583555 | + | 0.576594i | ||||
\(772\) | 4.56813e6 | − | 4.56813e6i | 0.275864 | − | 0.275864i | ||||
\(773\) | 1.03836e7 | − | 1.03836e7i | 0.625029 | − | 0.625029i | −0.321784 | − | 0.946813i | \(-0.604282\pi\) |
0.946813 | + | 0.321784i | \(0.104282\pi\) | |||||||
\(774\) | −49874.9 | + | 4.15569e6i | −0.00299247 | + | 0.249339i | ||||
\(775\) | −6.85039e6 | − | 6.54841e6i | −0.409695 | − | 0.391635i | ||||
\(776\) | 3.64236e6i | 0.217134i | ||||||||
\(777\) | 835074. | + | 5010.93i | 0.0496218 | + | 0.000297760i | ||||
\(778\) | 2.58056e6 | + | 2.58056e6i | 0.152850 | + | 0.152850i | ||||
\(779\) | −1.29027e7 | −0.761792 | ||||||||
\(780\) | −5.38127e6 | − | 1.28004e7i | −0.316700 | − | 0.753335i | ||||
\(781\) | −3.03915e6 | −0.178289 | ||||||||
\(782\) | 536655. | + | 536655.i | 0.0313818 | + | 0.0313818i | ||||
\(783\) | 481175. | − | 2.67268e7i | 0.0280478 | − | 1.55791i | ||||
\(784\) | − | 1.45269e7i | − | 0.844076i | ||||||
\(785\) | 1.38229e7 | − | 5.90896e6i | 0.800618 | − | 0.342245i | ||||
\(786\) | −4.26475e6 | − | 4.31625e6i | −0.246228 | − | 0.249201i | ||||
\(787\) | −6.79785e6 | + | 6.79785e6i | −0.391232 | + | 0.391232i | −0.875126 | − | 0.483894i | \(-0.839222\pi\) |
0.483894 | + | 0.875126i | \(0.339222\pi\) | |||||||
\(788\) | 7.21736e6 | − | 7.21736e6i | 0.414060 | − | 0.414060i | ||||
\(789\) | −6.17758e6 | − | 6.25216e6i | −0.353285 | − | 0.357551i | ||||
\(790\) | 1.91238e6 | − | 817498.i | 0.109020 | − | 0.0466035i | ||||
\(791\) | 3.08735e6i | 0.175447i | ||||||||
\(792\) | −4.74461e6 | − | 4.85988e6i | −0.268774 | − | 0.275304i | ||||
\(793\) | −255950. | − | 255950.i | −0.0144535 | − | 0.0144535i | ||||
\(794\) | 4.11709e6 | 0.231760 | ||||||||
\(795\) | 8.94568e6 | + | 2.12791e7i | 0.501990 | + | 1.19409i | ||||
\(796\) | −1.83420e7 | −1.02604 | ||||||||
\(797\) | 1.32048e7 | + | 1.32048e7i | 0.736354 | + | 0.736354i | 0.971870 | − | 0.235516i | \(-0.0756781\pi\) |
−0.235516 | + | 0.971870i | \(0.575678\pi\) | |||||||
\(798\) | 623458. | + | 3741.12i | 0.0346577 | + | 0.000207967i | ||||
\(799\) | 3.71513e6i | 0.205877i | ||||||||
\(800\) | −252006. | − | 1.11814e7i | −0.0139215 | − | 0.617690i | ||||
\(801\) | 2.57625e7 | + | 309192.i | 1.41875 | + | 0.0170273i | ||||
\(802\) | 3.13295e6 | − | 3.13295e6i | 0.171996 | − | 0.171996i | ||||
\(803\) | 4.19301e6 | − | 4.19301e6i | 0.229476 | − | 0.229476i | ||||
\(804\) | −1.93561e7 | + | 1.91252e7i | −1.05603 | + | 1.04343i | ||||
\(805\) | −115625. | + | 288289.i | −0.00628872 | + | 0.0156797i | ||||
\(806\) | − | 1.97456e6i | − | 0.107062i | ||||||
\(807\) | 120909. | − | 2.01495e7i | 0.00653542 | − | 1.08913i | ||||
\(808\) | 754938. | + | 754938.i | 0.0406802 | + | 0.0406802i | ||||
\(809\) | 9.33642e6 | 0.501544 | 0.250772 | − | 0.968046i | \(-0.419316\pi\) | ||||
0.250772 | + | 0.968046i | \(0.419316\pi\) | |||||||
\(810\) | 1.52340e6 | + | 3.81450e6i | 0.0815834 | + | 0.204280i | ||||
\(811\) | 2.41694e7 | 1.29037 | 0.645184 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645184 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(812\) | −2.43591e6 | − | 2.43591e6i | −0.129650 | − | 0.129650i | ||||
\(813\) | −73484.6 | + | 1.22462e7i | −0.00389915 | + | 0.649794i | ||||
\(814\) | 1.49559e6i | 0.0791136i | ||||||||
\(815\) | 1.17868e7 | + | 2.75731e7i | 0.621589 | + | 1.45409i | ||||
\(816\) | −1.71274e7 | + | 1.69231e7i | −0.900465 | + | 0.889723i | ||||
\(817\) | −1.94866e7 | + | 1.94866e7i | −1.02137 | + | 1.02137i | ||||
\(818\) | 2.63109e6 | − | 2.63109e6i | 0.137484 | − | 0.137484i | ||||
\(819\) | 2.03825e6 | + | 24462.3i | 0.106181 | + | 0.00127435i | ||||
\(820\) | −1.01673e7 | − | 4.07785e6i | −0.528046 | − | 0.211786i | ||||
\(821\) | 2.01715e7i | 1.04443i | 0.852813 | + | 0.522217i | \(0.174895\pi\) | ||||
−0.852813 | + | 0.522217i | \(0.825105\pi\) | |||||||
\(822\) | 1.21114e6 | + | 7267.52i | 0.0625191 | + | 0.000375152i | ||||
\(823\) | 1.86980e7 | + | 1.86980e7i | 0.962269 | + | 0.962269i | 0.999314 | − | 0.0370443i | \(-0.0117943\pi\) |
−0.0370443 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(824\) | −4.99115e6 | −0.256084 | ||||||||
\(825\) | 1.25923e7 | + | 1.21827e7i | 0.644127 | + | 0.623172i | ||||
\(826\) | −423802. | −0.0216129 | ||||||||
\(827\) | −2.18328e7 | − | 2.18328e7i | −1.11006 | − | 1.11006i | −0.993142 | − | 0.116916i | \(-0.962699\pi\) |
−0.116916 | − | 0.993142i | \(-0.537301\pi\) | |||||||
\(828\) | 1.79169e6 | + | 1.83521e6i | 0.0908209 | + | 0.0930274i | ||||
\(829\) | − | 1.09016e7i | − | 0.550941i | −0.961310 | − | 0.275470i | \(-0.911166\pi\) | ||
0.961310 | − | 0.275470i | \(-0.0888336\pi\) | |||||||
\(830\) | −2.80016e6 | − | 1.12307e6i | −0.141087 | − | 0.0565865i | ||||
\(831\) | −2.40549e7 | − | 2.43453e7i | −1.20837 | − | 1.22296i | ||||
\(832\) | −8.74504e6 | + | 8.74504e6i | −0.437979 | + | 0.437979i | ||||
\(833\) | −2.05932e7 | + | 2.05932e7i | −1.02828 | + | 1.02828i | ||||
\(834\) | 141489. | + | 143197.i | 0.00704381 | + | 0.00712886i | ||||
\(835\) | −6.59176e6 | − | 1.54202e7i | −0.327179 | − | 0.765373i | ||||
\(836\) | − | 2.19601e7i | − | 1.08672i | ||||||
\(837\) | 206779. | − | 1.14855e7i | 0.0102022 | − | 0.566678i | ||||
\(838\) | −486549. | − | 486549.i | −0.0239341 | − | 0.0239341i | ||||
\(839\) | −2.66932e7 | −1.30917 | −0.654585 | − | 0.755989i | \(-0.727156\pi\) | ||||
−0.654585 | + | 0.755989i | \(0.727156\pi\) | |||||||
\(840\) | 1.00513e6 | + | 410149.i | 0.0491499 | + | 0.0200559i | ||||
\(841\) | 2.92872e7 | 1.42787 | ||||||||
\(842\) | 4.89309e6 | + | 4.89309e6i | 0.237850 | + | 0.237850i | ||||
\(843\) | −1.94723e7 | − | 116845.i | −0.943731 | − | 0.00566294i | ||||
\(844\) | 2.75641e7i | 1.33195i | ||||||||
\(845\) | 2.02855e6 | − | 5.05780e6i | 0.0977338 | − | 0.243680i | ||||
\(846\) | 7660.97 | − | 638329.i | 0.000368008 | − | 0.0306633i | ||||
\(847\) | −359199. | + | 359199.i | −0.0172039 | + | 0.0172039i | ||||
\(848\) | 1.64408e7 | − | 1.64408e7i | 0.785115 | − | 0.785115i | ||||
\(849\) | 8.84534e6 | − | 8.73982e6i | 0.421158 | − | 0.416134i | ||||
\(850\) | −4.72825e6 | + | 4.94629e6i | −0.224467 | + | 0.234819i | ||||
\(851\) | − | 1.15826e6i | − | 0.0548255i | ||||||
\(852\) | 24068.4 | − | 4.01100e6i | 0.00113592 | − | 0.189302i | ||||
\(853\) | −1.62298e7 | − | 1.62298e7i | −0.763729 | − | 0.763729i | 0.213265 | − | 0.976994i | \(-0.431590\pi\) |
−0.976994 | + | 0.213265i | \(0.931590\pi\) | |||||||
\(854\) | 13798.7 | 0.000647432 | ||||||||
\(855\) | −1.04414e7 | + | 2.51555e7i | −0.488476 | + | 1.17684i | ||||
\(856\) | 5.19086e6 | 0.242133 | ||||||||
\(857\) | 1.20256e7 | + | 1.20256e7i | 0.559313 | + | 0.559313i | 0.929112 | − | 0.369799i | \(-0.120573\pi\) |
−0.369799 | + | 0.929112i | \(0.620573\pi\) | |||||||
\(858\) | −21905.6 | + | 3.65057e6i | −0.00101587 | + | 0.169294i | ||||
\(859\) | 8.22165e6i | 0.380169i | 0.981768 | + | 0.190084i | \(0.0608761\pi\) | ||||
−0.981768 | + | 0.190084i | \(0.939124\pi\) | |||||||
\(860\) | −2.15142e7 | + | 9.19679e6i | −0.991924 | + | 0.424024i | ||||
\(861\) | 1.14392e6 | − | 1.13028e6i | 0.0525883 | − | 0.0519610i | ||||
\(862\) | −2.79975e6 | + | 2.79975e6i | −0.128337 | + | 0.128337i | ||||
\(863\) | −1.99274e7 | + | 1.99274e7i | −0.910803 | + | 0.910803i | −0.996335 | − | 0.0855327i | \(-0.972741\pi\) |
0.0855327 | + | 0.996335i | \(0.472741\pi\) | |||||||
\(864\) | 9.75728e6 | − | 9.41216e6i | 0.444677 | − | 0.428948i | ||||
\(865\) | 3.83200e6 | − | 1.63809e6i | 0.174135 | − | 0.0744385i | ||||
\(866\) | − | 891970.i | − | 0.0404162i | ||||||
\(867\) | 2.61369e7 | + | 156837.i | 1.18088 | + | 0.00708598i | ||||
\(868\) | −1.04680e6 | − | 1.04680e6i | −0.0471591 | − | 0.0471591i | ||||
\(869\) | 1.07538e7 | 0.483075 | ||||||||
\(870\) | −7.05394e6 | + | 2.96546e6i | −0.315961 | + | 0.132829i | ||||
\(871\) | 2.99953e7 | 1.33970 | ||||||||
\(872\) | −3.17382e6 | − | 3.17382e6i | −0.141349 | − | 0.141349i | ||||
\(873\) | 8.14975e6 | − | 7.95645e6i | 0.361917 | − | 0.353333i | ||||
\(874\) | − | 864747.i | − | 0.0382922i | ||||||
\(875\) | −2.62205e6 | − | 983648.i | −0.115777 | − | 0.0434330i | ||||
\(876\) | 5.50063e6 | + | 5.56704e6i | 0.242188 | + | 0.245112i | ||||
\(877\) | 6.32074e6 | − | 6.32074e6i | 0.277504 | − | 0.277504i | −0.554608 | − | 0.832112i | \(-0.687132\pi\) |
0.832112 | + | 0.554608i | \(0.187132\pi\) | |||||||
\(878\) | −3.76868e6 | + | 3.76868e6i | −0.164988 | + | 0.164988i | ||||
\(879\) | 3.05704e7 | + | 3.09395e7i | 1.33453 | + | 1.35065i | ||||
\(880\) | 6.56959e6 | − | 1.63800e7i | 0.285977 | − | 0.713029i | ||||
\(881\) | − | 3.32918e7i | − | 1.44510i | −0.691319 | − | 0.722550i | \(-0.742970\pi\) | ||
0.691319 | − | 0.722550i | \(-0.257030\pi\) | |||||||
\(882\) | 3.58076e6 | − | 3.49583e6i | 0.154990 | − | 0.151314i | ||||
\(883\) | −5.57402e6 | − | 5.57402e6i | −0.240584 | − | 0.240584i | 0.576508 | − | 0.817092i | \(-0.304415\pi\) |
−0.817092 | + | 0.576508i | \(0.804415\pi\) | |||||||
\(884\) | 2.80399e7 | 1.20683 | ||||||||
\(885\) | 6.99478e6 | − | 1.71417e7i | 0.300204 | − | 0.735691i | ||||
\(886\) | −3.50924e6 | −0.150186 | ||||||||
\(887\) | −2.79973e7 | − | 2.79973e7i | −1.19483 | − | 1.19483i | −0.975693 | − | 0.219141i | \(-0.929674\pi\) |
−0.219141 | − | 0.975693i | \(-0.570326\pi\) | |||||||
\(888\) | −4.04805e6 | − | 24290.7i | −0.172272 | − | 0.00103373i | ||||
\(889\) | − | 1.59906e6i | − | 0.0678593i | ||||||
\(890\) | −2.89896e6 | − | 6.78156e6i | −0.122678 | − | 0.286982i | ||||
\(891\) | −509712. | + | 2.12321e7i | −0.0215095 | + | 0.895980i | ||||
\(892\) | 9.90573e6 | − | 9.90573e6i | 0.416845 | − | 0.416845i | ||||
\(893\) | 2.99322e6 | − | 2.99322e6i | 0.125606 | − | 0.125606i | ||||
\(894\) | 4.93590e6 | − | 4.87701e6i | 0.206549 | − | 0.204085i | ||||
\(895\) | −2.72078e7 | − | 1.09123e7i | −1.13536 | − | 0.455365i | ||||
\(896\) | − | 2.30742e6i | − | 0.0960189i | ||||||
\(897\) | 16964.8 | − | 2.82719e6i | 0.000703992 | − | 0.117321i | ||||
\(898\) | 461093. | + | 461093.i | 0.0190809 | + | 0.0190809i | ||||
\(899\) | 2.14002e7 | 0.883119 | ||||||||
\(900\) | −1.61782e7 | + | 1.65226e7i | −0.665768 | + | 0.679943i | ||||
\(901\) | −4.66128e7 | −1.91290 | ||||||||
\(902\) | 2.03651e6 | + | 2.03651e6i | 0.0833432 | + | 0.0833432i | ||||
\(903\) | 20610.1 | − | 3.43468e6i | 0.000841124 | − | 0.140174i | ||||
\(904\) | − | 1.49661e7i | − | 0.609097i | ||||||
\(905\) | 8.50852e6 | + | 3.41255e6i | 0.345329 | + | 0.138502i | ||||
\(906\) | 2.49788e6 | − | 2.46809e6i | 0.101100 | − | 0.0998941i | ||||
\(907\) | −4.07896e6 | + | 4.07896e6i | −0.164638 | + | 0.164638i | −0.784618 | − | 0.619980i | \(-0.787141\pi\) |
0.619980 | + | 0.784618i | \(0.287141\pi\) | |||||||
\(908\) | −2.18641e6 | + | 2.18641e6i | −0.0880068 | + | 0.0880068i | ||||
\(909\) | 40064.7 | − | 3.33827e6i | 0.00160824 | − | 0.134002i | ||||
\(910\) | −229357. | − | 536536.i | −0.00918137 | − | 0.0214781i | ||||
\(911\) | − | 1.63280e7i | − | 0.651833i | −0.945399 | − | 0.325917i | \(-0.894327\pi\) | ||
0.945399 | − | 0.325917i | \(-0.105673\pi\) | |||||||
\(912\) | 2.74339e7 | + | 164620.i | 1.09220 | + | 0.00655382i | ||||
\(913\) | −1.10307e7 | − | 1.10307e7i | −0.437952 | − | 0.437952i | ||||
\(914\) | −1.37713e6 | −0.0545268 | ||||||||
\(915\) | −227746. | + | 558122.i | −0.00899285 | + | 0.0220382i | ||||
\(916\) | 8.48615e6 | 0.334174 | ||||||||
\(917\) | 3.54597e6 | + | 3.54597e6i | 0.139255 | + | 0.139255i | ||||
\(918\) | −8.29306e6 | − | 149304.i | −0.324794 | − | 0.00584743i | ||||
\(919\) | 3.57465e7i | 1.39619i | 0.716005 | + | 0.698095i | \(0.245969\pi\) | ||||
−0.716005 | + | 0.698095i | \(0.754031\pi\) | |||||||
\(920\) | 560497. | − | 1.39749e6i | 0.0218325 | − | 0.0544351i | ||||
\(921\) | −1.10329e7 | − | 1.11662e7i | −0.428590 | − | 0.433765i | ||||
\(922\) | −1.51549e6 | + | 1.51549e6i | −0.0587119 | + | 0.0587119i | ||||
\(923\) | −3.12649e6 | + | 3.12649e6i | −0.120796 | + | 0.120796i | ||||
\(924\) | 1.92371e6 | + | 1.94694e6i | 0.0741243 | + | 0.0750192i | ||||
\(925\) | 1.04403e7 | − | 235303.i | 0.401196 | − | 0.00904218i | ||||
\(926\) | 8.58106e6i | 0.328862i | ||||||||
\(927\) | 1.09028e7 | + | 1.11677e7i | 0.416714 | + | 0.426838i | ||||
\(928\) | 1.78586e7 | + | 1.78586e7i | 0.680735 | + | 0.680735i | ||||
\(929\) | −6.93935e6 | −0.263803 | −0.131901 | − | 0.991263i | \(-0.542108\pi\) | ||||
−0.131901 | + | 0.991263i | \(0.542108\pi\) | |||||||
\(930\) | −3.03134e6 | + | 1.27437e6i | −0.114929 | + | 0.0483156i | ||||
\(931\) | 3.31831e7 | 1.25471 | ||||||||
\(932\) | −2.18156e6 | − | 2.18156e6i | −0.0822673 | − | 0.0822673i | ||||
\(933\) | 1.24964e7 | + | 74985.7i | 0.469981 | + | 0.00282016i | ||||
\(934\) | 9.41515e6i | 0.353151i | ||||||||
\(935\) | −3.25332e7 | + | 1.39072e7i | −1.21702 | + | 0.520247i | ||||
\(936\) | −9.88050e6 | − | 118582.i | −0.368629 | − | 0.00442414i | ||||
\(937\) | 1.00667e7 | − | 1.00667e7i | 0.374575 | − | 0.374575i | −0.494565 | − | 0.869141i | \(-0.664673\pi\) |
0.869141 | + | 0.494565i | \(0.164673\pi\) | |||||||
\(938\) | −808549. | + | 808549.i | −0.0300054 | + | 0.0300054i | ||||
\(939\) | −2.13872e7 | + | 2.11320e7i | −0.791569 | + | 0.782126i | ||||
\(940\) | 3.30465e6 | − | 1.41266e6i | 0.121985 | − | 0.0521457i | ||||
\(941\) | 1.13958e7i | 0.419536i | 0.977751 | + | 0.209768i | \(0.0672709\pi\) | ||||
−0.977751 | + | 0.209768i | \(0.932729\pi\) | |||||||
\(942\) | 31299.9 | − | 5.21613e6i | 0.00114925 | − | 0.191523i | ||||
\(943\) | −1.57718e6 | − | 1.57718e6i | −0.0577566 | − | 0.0577566i | ||||
\(944\) | −1.86485e7 | −0.681104 | ||||||||
\(945\) | −1.27792e6 | − | 3.14491e6i | −0.0465504 | − | 0.114559i | ||||
\(946\) | 6.15139e6 | 0.223483 | ||||||||
\(947\) | −2.70855e7 | − | 2.70855e7i | −0.981436 | − | 0.981436i | 0.0183949 | − | 0.999831i | \(-0.494144\pi\) |
−0.999831 | + | 0.0183949i | \(0.994144\pi\) | |||||||
\(948\) | −85164.4 | + | 1.41927e7i | −0.00307778 | + | 0.512913i | ||||
\(949\) | − | 8.62701e6i | − | 0.310953i | ||||||
\(950\) | 7.79460e6 | − | 175675.i | 0.280211 | − | 0.00631540i | ||||
\(951\) | 2.26680e7 | − | 2.23976e7i | 0.812759 | − | 0.803063i | ||||
\(952\) | −1.55011e6 | + | 1.55011e6i | −0.0554332 | + | 0.0554332i | ||||
\(953\) | 1.31117e7 | − | 1.31117e7i | 0.467656 | − | 0.467656i | −0.433498 | − | 0.901154i | \(-0.642721\pi\) |
0.901154 | + | 0.433498i | \(0.142721\pi\) | |||||||
\(954\) | 8.00893e6 | + | 96120.1i | 0.284907 | + | 0.00341935i | ||||
\(955\) | −1.16359e7 | + | 2.90118e7i | −0.412848 | + | 1.02936i | ||||
\(956\) | 3.29066e7i | 1.16450i | ||||||||
\(957\) | −3.95647e7 | − | 237412.i | −1.39646 | − | 0.00837958i | ||||
\(958\) | 2.36053e6 | + | 2.36053e6i | 0.0830990 | + | 0.0830990i | ||||
\(959\) | −1.00097e6 | −0.0351458 | ||||||||
\(960\) | 1.90693e7 | + | 7.78137e6i | 0.667817 | + | 0.272507i | ||||
\(961\) | −1.94327e7 | −0.678772 | ||||||||
\(962\) | 1.53857e6 | + | 1.53857e6i | 0.0536018 | + | 0.0536018i | ||||
\(963\) | −1.13390e7 | − | 1.16145e7i | −0.394013 | − | 0.403585i | ||||
\(964\) | 1.04257e7i | 0.361338i | ||||||||
\(965\) | 4.66161e6 | + | 1.09050e7i | 0.161145 | + | 0.376969i | ||||
\(966\) | 75752.0 | + | 76666.6i | 0.00261187 | + | 0.00264340i | ||||
\(967\) | −1.94460e7 | + | 1.94460e7i | −0.668751 | + | 0.668751i | −0.957427 | − | 0.288676i | \(-0.906785\pi\) |
0.288676 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(968\) | 1.74123e6 | − | 1.74123e6i | 0.0597267 | − | 0.0597267i | ||||
\(969\) | −3.86568e7 | − | 3.91235e7i | −1.32256 | − | 1.33853i | ||||
\(970\) | −3.02603e6 | − | 1.21366e6i | −0.103263 | − | 0.0414161i | ||||
\(971\) | 1.06222e7i | 0.361548i | 0.983525 | + | 0.180774i | \(0.0578603\pi\) | ||||
−0.983525 | + | 0.180774i | \(0.942140\pi\) | |||||||
\(972\) | −2.80176e7 | − | 840853.i | −0.951186 | − | 0.0285466i | ||||
\(973\) | −117642. | − | 117642.i | −0.00398366 | − | 0.00398366i | ||||
\(974\) | −8.14668e6 | −0.275159 | ||||||||
\(975\) | 2.54870e7 | − | 421433.i | 0.858632 | − | 0.0141977i | ||||
\(976\) | 607182. | 0.0204030 | ||||||||
\(977\) | 3.25074e7 | + | 3.25074e7i | 1.08955 | + | 1.08955i | 0.995575 | + | 0.0939726i | \(0.0299566\pi\) |
0.0939726 | + | 0.995575i | \(0.470043\pi\) | |||||||
\(978\) | 1.04048e7 | + | 62435.1i | 0.347847 | + | 0.00208729i | ||||
\(979\) | − | 3.81346e7i | − | 1.27163i | ||||||
\(980\) | 2.61483e7 | + | 1.04874e7i | 0.869719 | + | 0.348822i | ||||
\(981\) | −168435. | + | 1.40344e7i | −0.00558805 | + | 0.465609i | ||||
\(982\) | 4.93154e6 | − | 4.93154e6i | 0.163194 | − | 0.163194i | ||||
\(983\) | 342472. | − | 342472.i | 0.0113042 | − | 0.0113042i | −0.701432 | − | 0.712736i | \(-0.747456\pi\) |
0.712736 | + | 0.701432i | \(0.247456\pi\) | |||||||
\(984\) | −5.54522e6 | + | 5.47907e6i | −0.182571 | + | 0.180393i | ||||
\(985\) | 7.36505e6 | + | 1.72291e7i | 0.241872 | + | 0.565813i | ||||
\(986\) | − | 1.54519e7i | − | 0.506163i | ||||||
\(987\) | −3165.78 | + | 527579.i | −0.000103440 | + | 0.0172383i | ||||
\(988\) | −2.25912e7 | − | 2.25912e7i | −0.736288 | − | 0.736288i | ||||
\(989\) | −4.76395e6 | −0.154873 | ||||||||
\(990\) | 5.61848e6 | − | 2.32242e6i | 0.182193 | − | 0.0753101i | ||||
\(991\) | −2.24558e7 | −0.726346 | −0.363173 | − | 0.931722i | \(-0.618307\pi\) | ||||
−0.363173 | + | 0.931722i | \(0.618307\pi\) | |||||||
\(992\) | 7.67453e6 | + | 7.67453e6i | 0.247612 | + | 0.247612i | ||||
\(993\) | −15676.6 | + | 2.61251e6i | −0.000504521 | + | 0.0840786i | ||||
\(994\) | − | 168554.i | − | 0.00541096i | ||||||
\(995\) | 1.25342e7 | − | 3.12516e7i | 0.401364 | − | 1.00072i | ||||
\(996\) | 1.46454e7 | − | 1.44707e7i | 0.467793 | − | 0.462213i | ||||
\(997\) | 2.66705e7 | − | 2.66705e7i | 0.849755 | − | 0.849755i | −0.140347 | − | 0.990102i | \(-0.544822\pi\) |
0.990102 | + | 0.140347i | \(0.0448220\pi\) | |||||||
\(998\) | 3.98429e6 | − | 3.98429e6i | 0.126627 | − | 0.126627i | ||||
\(999\) | 8.78832e6 | + | 9.11056e6i | 0.278607 | + | 0.288823i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 15.6.e.a.8.5 | yes | 16 | |
3.2 | odd | 2 | inner | 15.6.e.a.8.4 | yes | 16 | |
5.2 | odd | 4 | inner | 15.6.e.a.2.4 | ✓ | 16 | |
5.3 | odd | 4 | 75.6.e.e.32.5 | 16 | |||
5.4 | even | 2 | 75.6.e.e.68.4 | 16 | |||
15.2 | even | 4 | inner | 15.6.e.a.2.5 | yes | 16 | |
15.8 | even | 4 | 75.6.e.e.32.4 | 16 | |||
15.14 | odd | 2 | 75.6.e.e.68.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.6.e.a.2.4 | ✓ | 16 | 5.2 | odd | 4 | inner | |
15.6.e.a.2.5 | yes | 16 | 15.2 | even | 4 | inner | |
15.6.e.a.8.4 | yes | 16 | 3.2 | odd | 2 | inner | |
15.6.e.a.8.5 | yes | 16 | 1.1 | even | 1 | trivial | |
75.6.e.e.32.4 | 16 | 15.8 | even | 4 | |||
75.6.e.e.32.5 | 16 | 5.3 | odd | 4 | |||
75.6.e.e.68.4 | 16 | 5.4 | even | 2 | |||
75.6.e.e.68.5 | 16 | 15.14 | odd | 2 |